When you are mixed, you are considered to be what ever ethnicities you are mixed with. For example, I am mixed with Asian and White so I consider myself Asian and white. Often times, people disregard one of the races and just refer to themselves as white, or black, or Asian and I do not think that is right.
They should be consider multi-racial or bi-racial like they are. If they ask to be identified white, than they'll be white. If they ask to be identified black, they'll be black. Some mixed children don't even know either the black or the white side of their family which also factors in. I believe that if they don't identify as one race while growing up than they'll have the characteristics and qualities of both/all races they are.