"Beau came in, he's the oldest," Joe Biden said. "He's a year and a day older than Hunter, and he said, 'Daddy, Hunter has something to tell you.' And Hunter said, 'No, Dad, Beau has something to tell you.' ... And I said, 'Guys what is it?' Finally, Beau said, 'Daddy we were talking and we think we should marry Jill.'"
Jill Biden joked that her sons were "the easiest part of the marriage."
"When I met Joe, I think you know I fell in love with the boys, and I think everyone wanted a family," she said. "I mean, it was obvious, and they were just so easy to love."
Jill Biden gave up her teaching career to become a full-time mother to Beau and Hunter and, in 1981, to daughter Ashley.
"I did the mom things, you know," she said. "I did hot dog day at the school, worked at the library and all those sorts of things. And it worked."
Given the tragedy in his life, Joe Biden said that he and his wife have taught their children not to take anything for granted and never go to sleep angry.
"We have a deal," he said.. We can never go to bed angry, because in my life experience you don't want to be. You don't want to leave one another.
"I will not leave the house, I swear to God, until she kisses me and gives me a hug when we've had a fight," he said, "because you never know what's going to happen.
"I know in my own life experience, I think to myself what would have happened in my previous circumstance had I had a big fight and then something happened," he said.
Both Bidens agreed that one of the keys to a successful marriage was putting it ahead of a career.
"Once you think your career is more important than your marriage, then it leads you [down] a path," the vice president said. "Because if your career's that important, then ... it's just trouble."
Since the start of the Obama administration, the Bidens are able to spend more time together at work and at home.
That Joe Biden commuted back and forth daily between the Senate in Washington and his home in Wilmington, Del., to be with his family is well known -- but because of the long hours, he noted, he was seldom home in time for dinner.
One of the advantages of living and working in Washington full-time, he said, is "almost every night we get to have dinner together."
"She jokes, the reason a marriage works so well [was that] I wasn't home every night," Biden said.
Jill Biden keeps an office in the Eisenhower Executive Office Building. When she is there, her husband often tries to sneak over for a few minutes and have lunch or say hello.
"I just drive her nuts, because she needs some space," he said. "But when she's in, I say, 'Well, why don't I go over and have lunch with her,' and they say, 'No, she's got something to do ... no, she's kind of busy right now,'
"It's like, 'Well why can't -- look, it's only across the street. Why can't I go eat my soup over there?'" he said.
"And my staff says, 'He's coming over again,'" his wife said.
At the event announcing his name on the Obama presidential ticket, Biden introduced wife Jill to the nation, and as it sometimes does, his candid nature landed him in some trouble.
Biden called his wife "drop-dead gorgeous" and jokingly referred to his wife's Ph.D. as a "problem." He soon took some heat from people who said his remark was sexist.
But looking back, Jill Biden said she did not see what the fuss was about.