Henne completed 16-of-36 passes for 354 yards and four scores after subbing for injured starter Blaine Gabbert in Sunday's overtime-loss to the Houston Texans.
Gabbert sustained an elbow injury in the first quarter and did not return.
"Chad Henne executed the game plan really well on Sunday," Mularkey said.
Henne has started 31 of the 40 games he has played in the NFL the past five seasons. He has 7,683 yards, 36 touchdowns and 38 interceptions for his career.