They started out as political opponents, but they say they will leave office as close friends.

For the past eight years, President Barack Obama and Vice President Joe Biden have been an inseparable political duo. They have seen the country -- and each other -- through the best and worst times.

"He always kids me. I'm always saying, 'All politics is personal.' By that I mean, if you understand the other man's hopes, aspirations, fears -- the president and I, we know each other. We talk. We have lunch every week. Probably 60 percent of the time, we talk about our families," Biden told "CBS This Morning" co-host Charlie Rose. "He was there for my son. He was the only one, when my son was dying, that I was able to be completely candid with."

The vice president said he felt obliged to let Mr. Obama know what was going on as his son Beau battled brain cancer.

"He was genuinely moved. And, 'Joe, what do you need?' ... So it's a genuine friend -- I respect him," Biden said. "He has more backbone, more character than any one person -- and there are a lot of presidents with character -- than any president I've dealt with, the last eight presidents. I trust him."

Biden said an added advantage they have is that their families are close.

"My granddaughters are the very best friends of his daughters," he said.

The president jokes and says they make up for each other's shortcomings, Biden said.

"He makes up for a lot more of my shortcomings than I do his, number one," Biden added.

But they also have different styles and experiences in government.

"So when he asked me to join him, I asked him why. He said, 'I want you to help me govern because you know the system.' ... Whomever the next president is should have somebody they trust, they know will have their back. They understand they're vice president, not president -- and will be candid with them," Biden said. "And the deal we made, when we did this, he said, 'Do you have any conditions?' I said, jokingly, I said, 'Two things: I'm not wearing any funny hats, and I'm not going to change my brand.' ... We holler at each other in private meetings ... just like two friends."