The Obamas: How We Deal with Our Own Racist Experiences

The Obamas open up about raising their daughters, the impact of stereotypes, and what's on the POTUS dance party playlist. Subscribe now for instant access to the exclusive PEOPLE interview.

The protective bubble that comes with the presidency – the armored limo, the Secret Service detail, the White House – shields Barack and Michelle Obama from a lot of unpleasantness. But their encounters with racial prejudice aren't as far in the past as one might expect. And they obviously still sting.

"I think people forget that we've lived in the White House for six years," the first lady told PEOPLE, laughing wryly, along with her husband, at the assumption that the first family has been largely insulated from coming face-to-face with racism.

"Before that, Barack Obama was a black man that lived on the South Side of Chicago, who had his share of troubles catching cabs," Mrs. Obama said in the Dec. 10 interview appearing in the new issue of PEOPLE.

"I tell this story – I mean, even as the first lady – during that wonderfully publicized trip I took to Target, not highly disguised, the only person who came up to me in the store was a woman who asked me to help her take something off a shelf. Because she didn't see me as the first lady, she saw me as someone who could help her. Those kinds of things happen in life. So it isn't anything new."

In a 30-minute conversation, the president and Mrs. Obama candidly added their stories to the national discussion of race and racial profiling that was sparked by the deaths of Michael Brown in Ferguson, Missouri, and Eric Garner in Staten Island, New York.

"There's no black male my age, who's a professional, who hasn't come out of a restaurant and is waiting for their car and somebody didn't hand them their car keys," said the president, adding that, yes, it had happened to him.

Mrs. Obama recalled another incident: "He was wearing a tuxedo at a black-tie dinner, and somebody asked him to get coffee."

Things have gotten better, both Obamas agreed, but there's still more progress to be made.

"The small irritations or indignities that we experience are nothing compared to what a previous generation experienced," President Obama said. "It's one thing for me to be mistaken for a waiter at a gala. It's another thing for my son to be mistaken for a robber and to be handcuffed, or worse, if he happens to be walking down the street and is dressed the way teenagers dress."

For more from our exclusive interview with the president and first lady, pick up the new issue of PEOPLE, on newsstands Friday