Milley has spent much of the past two days fending off often personal attacks from Republicans during acrimonious hearings on the withdrawal from Afghanistan over his calls with China and interviews for books critical of Donald Trump's presidency.
Many members of the Senate and House Armed Services committees devoted their time to questions about Milley's interviews with Bob Woodward and other authors rather than to the 20-year U.S. involvement in Afghanistan, and its chaotic and deadly end last month.
Several asked why Milley had not resigned, and one suggested that if he were in China, he might be shot.
Cheney, one of only two Republicans on a select committee investigating the January attack, apologized to Milley while criticizing those who tried to "whitewash" the riot.
Cheney said many U.S. officials had failed to do their duty.
"For any member of this committee, for any American to question your loyalty to our nation, to question your understanding of our Constitution, your loyalty to our Constitution, your recognition and understanding of the civilian chair of command is despicable," Cheney told Milley.
"I want to apologize for those members of this committee who've done so," Cheney said. "And I want to thank you for standing in the breach, when so many, including many in this room, failed to do so."