Getting them to do both at the same time, however, has proven elusive over the past month as the Chiefs dropped three of their last four games.
"I've seen it before the last couple of games here where both sides were playing well at the same time," Reid said. "When we do that we're a tough team to stop. We've got to continue to do that."
In the team's 28-17 loss to the Dallas Cowboys on Sunday, the split personality of both squads alternated the stage with one another.
"I thought we were up and down," Reid said. "The defense I thought started real well, the offense didn't. Then the second half, the offense picked it up and the defense had a couple of drives there."
During the first five weeks of the season, the Chiefs could do no wrong. The team raced to a 5-0 start with the offense piling up the points and the defense making timely stops.
But in recent weeks, neither offense nor defense consistently fired on all cylinders.
One curious struggle for the offense comes from the rushing game. Rookie Kareem Hunt, who leads the league with 800 yards rushing, mustered only 37 yards rushing on nine carries.
That continued a four-game streak during which Hunt averaged only 48 yards per game. He averaged 121.8 yards through the team's first five games.
"Yesterday, we didn't run nearly as well as we should have, and they were doing some things to try and stop that," Reid said. "But even with that, you should still be effective."
Defensively, the Chiefs are struggling finding a balance against the run and pass. The Cowboys found a bit of balance, rushing for 131 yards and passing for 249, close to Kansas City's averages on the season. But often the Chiefs' defense cracks down on the run and surrenders a big passing day, or stiles the pass and gets gashed on the ground.
"If you get beat on a play, it doesn't matter what side of the ball you're on or special teams, it doesn't matter," Reid said. "You step back up and you challenge again. That's what you do. We've got to get back to do that better. Both sides of the ball."
Reid believes his team has the potential to put everything together, much as it did during the first five games of the season.
"I know what kind of talent we have," Reid said. "I'm confident in that. I've got to make sure offensively, defensively, special teams we're all doing the right things and were doing the part from a coaching standpoint where we're giving our players the best opportunity to make plays."
Cornerback Steven Nelson played 64 of Kansas City's 67 defensive snaps in Sunday's 28-17 loss to the Dallas Cowboys, marking another step since his return from injured reserve with a core muscle injury.
"Nelson's just kind of getting back into the swing of things," head coach Andy Reid said. "He's been playing the nickel position, playing a little bit of corner. We'll put him back in where he has a bigger role out there."
In his season debut against Denver in Week 8, Nelson played exclusively as the nickel back. Now the Chiefs are working him back in as their every-day right cornerback. He then moves to the slot when the team moves to a nickel or dime defense.
Nelson received a flag for pass interference in Sunday's loss to the Cowboys, but Reid faulted the call and not his cornerback. Nelson and Cowboys receiver Dez Bryant tangled up on the third-and-9 play. The penalty kept the Dallas drive alive, which culminated with a 2-yard touchdown run by Ezekiel Elliott putting the Cowboys up 21-17.
"I thought Nelson had the right of way on that and was called for pass interference," Reid said. "I didn't think that was. It ended up being a big play on that drive. It didn't allow us to get off the field and get back on when we had a little bit of momentum."
Third down proved a crucial situation for the Chiefs in their loss to Dallas, with the Cowboys converting 7-of-12 third-down attempts, with each one seemingly a crucial blow to Kansas City's efforts to get their defense off the field.
"Third downs we didn't get off the field," Reid said. "From a defensive standpoint we've got to be able to do that. We're better than that."
Reid faulted both sides of his team for failing on third down Sunday. The offense converted only 4-of-11 third-down tries. He wants his coaches to use the bye week to evaluate the team's struggles on third down and find solutions.
"Are we putting the guys into the right position to make plays on the ball, then are you making the play?" Reid asked. "We all take responsibility for that. We'll get that straightened out."
Chiefs head coach Andy Reid holds a 16-2 record following the bye week, yet his philosophy for the time off remains staggeringly simple: vacation time.
"I think it will be good for the players to get away," Reid. "I gave them this week off, step back, get away, heal up a little bit."
Rest comes at a critical junction for the Chiefs. The team bolted out of the gates to a 5-0 start but stumbled over the last month, falling to 6-3 heading into the bye.
"We've had a pretty good schedule up to this point and really have maximized themselves up to this point," Reid said. "The effort's been there and it's good to step back here to give them the opportunity to do that."
Another key to Reid's bye-week success is himself and his coaching staff. Reid carries a strong reputation for developing effective game plans given time to prepare. Now the Chiefs have nearly two weeks preparing for a road trip to visit the New York Giants.
"The coaches will work and take a couple of days off too and then get back on it and get ready for New York," Reid said.
NOTES: DE Allen Bailey left Sunday's game with a sprained MCL in his knee. He briefly tried to return to the game without success. The plans are for Bailey to undergo additional tests to determine the extent of the damage. ... LB Tamba Hali made his season debut Sunday against Dallas, playing 23 of the team's defensive snaps. The team wants to evaluate how Hali's knees respond to his playing time and hope the bye week provides a slow immersion back onto the field. ... RG Laurent Duvernay-Tardif returned to the starting lineup after missing four games with a sprained knee. Sunday's game marked the first time the Chiefs returned its opening-week lineup to the field since Week 2 of the season. Duvernay-Tardif received a flag for a false start and head coach Andy Reid said he showed some rust, but was pleased with his overall performance. ... LB Dee Ford missed his third game this season with back issues, and the team has yet to indicate a time table for his return. The team hopes the bye week provides additional rest for Ford heading to the season's stretch drive. ... WR Albert Wilson did not play Sunday after aggravating a hamstring injury last week against Denver. It's not known how long the injury will keep Wilson on the sideline.
MOST VALUABLE ROOKIE: RB Kareem Hunt. The third-round pick from Toledo made a case as the league's MVP through the first quarter of the season. He leads the league with 800 yards rushing and 1,131 yards from scrimmage. Hunt's contact balance that allows him extend plays and his proficiency out of the backfield are not surprises. But the ease with which he made the transition to the pro level does raise some eyebrows, especially his ability to provide pass protection. Hunt's recent struggles on the ground, however, coincide with Kansas City dropping three of its last four games. Hunt averaged just 48 yards rushing in those games. Hunt remains the key to putting the Chiefs' offense back on track for the second half of the season.
VETERAN SURPRISE: LB Frank Zombo. The Chiefs rely on Zombo as a staunch run defender and sure tackler, but the team needed more from Zombo with a spate of injuries at outside linebacker and the 30-year-old veteran responded. With injuries limiting the playing time of Justin Houston, Dee Ford and Tamba Hali, Zombo stepped in to fill the breach, collecting 1.5 sacks and combining for 22 tackles through nine games. Zombo also serves as a mentor to the team's young linebackers, especially second-round draft pick Tanoh Kpassagnon.
MIDSEASON REPORT CARD
--PASSING OFFENSE: A-minus - Quarterback Alex Smith posted among the strongest first halves of his career, completing 69.6 percent of his passes for 2,444 yards and 18 touchdowns in the team's first nine games. All those numbers put him well on pace for career highs. Tight end Travis Kelce and wide receiver Tyreek Hill remain on pace for 1,000-yard receiving seasons, and rookie running back Kareem Hunt provides the team with a dual-threat option out of the backfield. The Chiefs lead the league at 6.2 yards per play, and Smith and the passing game are the biggest reason why.
--RUSHING OFFENSE: A-minus - The run game behind rookie Kareem Hunt deserve an A-plus for the first five games of the season, but the last four weeks bring down the average a bit. Hunt leads the league in rushing and yards from scrimmage, piling up 800 yards on the ground and adding 331 more through the air along with six touchdowns in total. Few running backs in recent weeks bolted out of the gates faster than Hunt. But with just 48 yards rushing per game the last four weeks, Hunt must find a way to make adjustments, as the league seems to be solving the riddle he poses.
--PASS DEFENSE: C-minus - The Chiefs rank 28th in passing yards allowed per game. The secondary missed two starters most of the first half of the season. Safety Eric Berry went to injured reserve with an Achilles tendon rupture following Week 1, and starting right cornerback Steven Nelson missed the team's first eight games with a core muscle injury. Perhaps most distressing, the Chiefs' pass rushing ranks tied for 16th with just 19 sacks through the first nine games. The team's defense relies on a strong pass rush to disrupt the passing game. When the Chiefs get to the quarterback, the defense can play lights out. When they cannot, opposing quarterbacks have big days.
--RUSH DEFENSE: D-minus - Even when teams don't rush the ball particularly well, they still seem to find ways to pile up yards against the Chiefs. The teams ranks 30th in the league with 131.1 rushing yards allowed per game. They also allowed nine rushing touchdowns, showing signs that the bend-but-don't-break defensive philosophy needs repairs quickly. The Chiefs seem to have the pieces to be better against the run, especially with the addition of defensive tackle Bennie Logan and linebacker Reggie Ragland. The team again misses the expertise of safety Eric Berry against the run.
--SPECIAL TEAMS: B-plus - The kicking game has been close to perfect with rookie kicker Harrison Butker connecting on his last 19 straight field-goal attempts. Punter Dustin Colquitt carries a less than stellar 39.4 net punting average but his ability to put the ball inside the 20 remains among the best in the league. Special teams coordinator Dave Toub normally hangs his hat on the return game, but the Chiefs have struggled in that area. The Chiefs rank eighth in kickoff returns with a 23.3-yard average. Teams normally avoid punt returner Tyreek Hill, leaving the Chiefs 17th in the league with an 8.2-yard return average.
--COACHING: B - Head coach Andy Reid and his staff deserve much of the credit for the team's 5-0 start, but it also holds significant ownership in the 1-3 slump leading to the bye week. Defensive coordinator Bob Sutton finds himself the target of much of the criticism with the team ranking 28th against the pass, 30th versus the run and 20th with 23.1 points allowed per game. The Chiefs have a Super Bowl offense and a No. 1 overall draft pick defense. Finding a way to improve the defense in the second half stands between the Chiefs and postseason success.