President Obama, Secretary of State Clinton Discuss "Improbable" Friendship on 60 Minutes

President Barack Obama and Secretary of State Hillary Clinton appeared on 60 Minutes Sunday night to discuss Clinton's impending departure from the administration and the unlikely partnership the two forged after a contentious primary campaign in 2008.

It was the president's idea to have the two sit down together for the interview. "I just wanted to have a chance to publicly say thank you, because I think Hillary will go down as one of the finest secretary of states we've had," Obama told Steve Kroft. "I want the country to appreciate just what an extraordinary role she's played during the course of my administration and a lot of the successes we've had internationally have been because of her hard work."

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Obama, who nominated Sen. John Kerry to replace Clinton, added that he "wished she was sticking around," and Clinton expressed a similar feeling. "This has been just an extraordinary opportunity to work with him as a partner and friend, to do our very best on behalf of this country we both love," Clinton said of the president. "And it's something I'm going to miss a great deal."

Just a few years ago, hearing those remarks would have been unimaginable, as the two engaged in heated, often bitter debates as they vied for the presidential nomination in 2008. Despite their back-and-forth, however, "we could never figure out what we were different on," Obama said.

"Look, in politics and in democracy, sometimes you win elections, sometimes you lose elections," Clinton explained. "And I worked very hard, but I lost. And then President Obama asked me to be secretary of state and I said yes. ... After I ended my campaign, I immediately did everything I could to help the president get elected, because despite our hard-fought primary, we had such agreement on what needed to be done for our country."

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After much courting by Obama, Clinton said her decision to join the administration came after the simple realization that she would have wanted him to do the same for her. "I thought, 'You know, if the roles had been reversed, and I had ended up winning, I would have desperately wanted him to be in my cabinet," Clinton said. "So if I'm saying I would have wanted him to say yes to me, how am I going to justify saying no to my president? And it was a great decision, despite my hesitancy about it."

Calling Clinton "one of the most important advisors that I've had on a whole range of issues," the president said she brought a sense of "professionalism and teamwork" to the inner workings of his cabinet. And while both stopped short of speculating on the 2016 presidential election (for which Clinton is considered a front-runner to win the Democratic nomination), it's clear their relationship — at least for the time being — is one of mutual support.

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"I think there's a sense of understanding [between us] that  sometimes doesn't even take words because we have similar views," Clinton said. "We have similar experiences that I think provide a bond that may seem unlikely to some, but has been really at a core of our relationship over the last four years."

Watch their full interview below: