Almost everyone is 'racially mixed' - in fact, there's not really much of a hard line between one 'race' and another. Just different population groups diverging slightly over long periods of time. Racial identity is a combination of self-identification, ancestry, and judgement by other people. As far as I'm aware, Mr. Obama self-identifies as black (I couldn't find a reference to this). His ancestry is mixed, but no more mixed than many other people defining themselves as african-american or black. Most people, looking at a picture of him, would probably identify him as black.
A good reference:
http://www.samefacts.com/archives/ba...bama_black.php