Bland, a 48-year-old from England, had a 4-under 67 and walked off the course at the top of the leaderboard in just his fourth major.
Henley had an opportunity to build a two-shot lead when he faced an 18-foot birdie putt on the par-5 ninth hole. He missed the shot, then watched his 2-foot par putt spin out of the cup. That gave him a 70 on the second day to join Bland at 5-under par for the tournament.
2010 British Open champion Louis Oosthuizen (71), coming off a runner-up finish in the PGA Championship, and Matthew Wolff (68), last year's U.S. Open runner-up at Winged Foot, both were one shot back of Bland and Henley.
Defending U.S. Open champion Bryson DeChambeau and his heated rival, Brooks Koepka, were at even-par 142, only five strokes behind the lead. Justin Thomas (69) and Collin Morikawa (67) also were at even par.
"Most times if I'm five back going into a Saturday, I need to probably make 12, 15-plus birdies on the weekend to hang in there," Thomas said. "But this is a U.S. Open. It's a little bit different."
Dustin Johnson and Rory McIlroy were headed in the wrong direction on the second day of the tournament. Johnson, who failed to make the cut in the Masters and the PGA Championship, slipped to 4-over par until a late rally gave him a 73 and entry into the weekend.
Similarly, McIlroy had to card two birdies down the stretch for a 73. Johnson was seven behind, while McIlroy was six back of the lead.