Henne showed mobility in the pocket and completed 12-of-17 passes before leaving with a 13-7 lead in the second quarter.
But he also plans to give Bortles some snaps with the first team, possibly in the coming week.
The rookie looked sharp again after an impressive showing last week in a victory over Tampa Bay. The No. 3 pick in the draft, Bortles went 11 for 17, but the Jaguars came away with the loss.
Clausen got the first call after Cutler left the game, with Palmer serving as the second man in relief in a flip from the preseason opener. But Clausen struggled through some headset problems after a strong performance last week.
"There were three to five plays where it just became confusion and he really didn't get us into the best plays," coach Marc Trestman said. "He was trying to make something good out of a bad situation, and there wasn't any way I could help him. That group of I would say up to a half a dozen plays when Jimmy was in there, it was very difficult to evaluate."
Palmer started the fourth quarter and threw for 73 yards, completing 6-of-9 passes.
"This is a competition and coaches have done a phenomenal job of making it very fair, evaluating us every day and so when you get to the preseason, you wait until your turn and then you go in there and try to make the most of it," Palmer said.
Marqise Lee caught four passes for 27 yards and a touchdown after struggling against Tampa Bay. Mercedes Lewis had 46 yards on three receptions.
The Bears cut it to 13-7 early in the second quarter, when Cutler hit Marshall with a 4-yarder to cap a 10-play drive. But a 43-yard field goal by Scobee late in the half made it 16-7.
"Definitely the first couple of drives we wanted to get the tempo going," Henne said. "The way we did that was first and second down. We moved the chains and got some explosive plays out of it as well."
Notes: Trestman said he has no issue with Marshall serving as an analyst for Showtime's "Inside the NFL" show. "I trust Brandon," he said. "He asked me about it. I trust him to make a decision that was in the best interest of the team first, and I know Brandon. I know he'll do that." ... Trestman had few details on CB Kyle Fuller (ankle) and backup TE Zach Miller (foot) after they left the game with injuries. He did say the bruised knee that kept DE Willie Young out of the game is not serious. ... Jaguars RT Austin Pasztor (broken hand) and backup C Luke Bowanko (sprained ankle) left the game.
Copyright 2014 by The Associated Press