You can say 'mixed race', but you had better do it carefully. Too many people here are looking for a reason to be aggrieved.
"Michelle Obama is black" is fine. Every once in a while there is a small backlash against "black", but it remains the safest.
Today a woman came in to the store and was discussing flowers with my son. She put off a final decision, saying she wanted to get her husband involved in deciding. My son told her "Fine, have him come and see me". The woman snarled that she would have HER see my son. So the womans husband is a woman, which is fine but how the hell are we supposed to keep up with the individual pronoun choices? Sometimes it seems people are looking for a reason to get angry.
My father always told me not to offend gay people, we have a sizable community near us and in my dad's words: "Them homos got a lot of money". Sigh. He did live in a simpler time.