I notice some biracials get offended by that term, some really could care less.
In 1961 when Obama was born, there was no such term or status as Mulatto on the U.S. Census- except for a few Censuses, you could only be black or white. That is the history of this country- we are not South Africa or Latin America, we are the United States, and we had the one drop rule. I doubt that the term "biracial" was even used prior to about 15-20 years ago.
If you saw Obama in the street, without knowing his background, you would think he was just a black guy, not "biracial".