A farewell interview with Mike Mullen

At a change-of-command ceremony this past week, President Obama had nothing but praise for Admiral Mike Mullen, the just-retired Chairman of the Joint Chiefs of Staff. Admiral Mullen has been speaking out a lot this week, too ... as we hear in our Cover Story from CBS News national security correspondent David Martin:

You wouldn't think the nation's highest ranking officer would be a regular on "The Daily Show," but in his final days as chairman he was back for a third appearance.

Last summer Admiral Mike Mullen recruited "Daily Show" host Jon Stewart to go with him to visit the troops in Afghanistan: "I was surprised when we landed in Kandahar that you forced them to carry you around on a litter," said Stewart.

"Actually that usually only happens once a trip," Mullen laughed.

After the "Daily Show" taping, Martin asked Mullen for an assessment of his host: "Good. Good. I mean, he does his homework."

When asked what he gets out of appearing on a Comedy Central satirical news TV show, Mullen replied, "Well, I get an opportunity to address an audience that in many cases may not be really familiar with the military and what we've been through.

"It's a much younger audience and it's a very popular audience. And it's been an opportunity with him to connect with a very popular guy who can also be a voice for our men and women and their families, and he clearly is."

Stewart was similarly complimentary of his guest: "He always does great, the man is charming," he said.

Well, not always. His staff says when he's tired he can be grumpy. And with his schedule he is frequently tired. In addition to all the things you expect the President's chief military adviser to do, he is constantly trying to connect with wider audiences - going on daytime talk shows, appearing with Muppets, and traveling to campuses to tell people what life is really like for soldiers and their families ...

"If I'm a 15-year-old boy or girl in that family and I was four or five when these wars started, my whole life in my family has been at war. That's never happened before," he told the audience at the University of Miami.

When he first started reaching out he was shocked at how little people really know about the sacrifices the one percent who serve are making - and what service members have been through - the number of deployments, stress on families, the suicide rates.

People who know the details, like retired Sgt. Jarrad Turner, who couldn't get the V.A. to pay for his surgery after being wounded in Iraq, frequently give him an earful:

"You got men and women and wives and kids and they're suffering. We've got to do better, sir," Turner said.

"Well, that's why I'm here," Mullen responded.

Everyone agrees wounded soldiers deserve the best possible care. But the stand Mullen took on gays serving openly put him at odds with some of the top commanders. They were worried about its effect on readiness.

He saw it differently.

"It's fundamentally an integrity issue

"Did it ever occur to you when you became chairman that you would end up being an agent of cultural change?"

"I hadn't thought about that."

In fact, it had never occurred to him that he would become Chairman. He was planning to retire as Chief of Naval Operations, until the day then-Secretary of Defense Gates called him into his office.

"Within about, oh, I don't know, 30 seconds, I could tell where he was going," Mullen recalled. "And I, uh, sort of got into one of these slow motion, 'Is this really happening' kind of feelings."

"And why did he tell you he was turning to you?"

"In particular something I had said that got his attention, which I felt that our Army was the center of gravity of our military - and he thought that was pretty significant coming from the Navy chief."

An Admiral suddenly thrust into the middle of two land wars, he immediately took off for Iraq and Afghanistan to see for himself.