The former president would like to work with Mrs. Obama, in her "after life" on veterans' issues, he tells PEOPLE.

George W. Bush Breaks Down His Affection for Michelle Obama: 'We Just Took to Each Other'

To some, they might seem an unlikely twosome: a former president and former first lady from two different administrations, different political parties, different generations and different upbringings.

But George W. Bush tells PEOPLE that he feels a real fondness for Michelle Obama.

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“She kind of likes my sense of humor. Anybody who likes my sense of humor, I immediately like,” says Bush, in an interview to launch his first art book and new exhibit, Portraits of Courage: A Commander in Chief’s Tribute to America’s Warriors, a collection of his paintings of post-9/11 war veterans.

Bush, 70, notes that he was regularly seated beside Obama, 53, at official events like Nancy Reagan’s memorial service, an interfaith memorial service for Texas police officers last year, and the September 2016 dedication ceremony in Washington, D.C., to mark the opening of the Smithsonian’s National Museum of African American History and Culture. There, photos of the two of them cuddling on stage went viral.

Image zoom ZACH GIBSON/AFP/Getty

“I can’t remember where else I’ve sat next to her, but I probably have a few wise cracks and she seemed to like it okay,” says Bush. “I needle her a little bit and around her, I’m fairly lighthearted. [The Obamas] are around serious people all the time and we just took to each other.”

Asked about that sweet moment at the Smithsonian, he says: “When I saw her, it was a genuine expression of affection.”

Image zoom Eric Gay/AP

And then there’s the work with military personnel, military families and veterans that Obama did as first lady through her Joining Forces initiative with Dr. Jill Biden, wife of the former vice president. That’s right up Bush’s alley. He has dedicated most of his post-presidency to the cause of wounded warriors—ensuring through wellness and employment programs at the George W. Bush Presidential Center that those wounded in war get the health and career assistance they need to make a full and successful transition to civilian life.

There, he and his wife Laura say, is where they hope to work with both Michelle and Barack Obama.

RELATED VIDEO: Click HERE to watch People Features: George W. Bush, Portraits of Courage

“I think they’re interested in, also, doing things with our troops of course now in their after-life, as I call it,” says Mrs. Bush.

Adds the former president: “It’s going to take them a while to find their footing and figure out how they’re going to do what they want to do. But if there’s a way to be symbiotic, we’ll do so.”