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.