We generally let people self-define in this country.
For many generations the term biracial didn't exist. I think it was in just that last couple of years that you were allowed to pick more than one race on the census forms. Americans don't like maybes, they like either/ors. So you are black or white, and can't be both. Seems silly to me, but that is how it has been historically.
Now we allow more nuance. I have a friend who is an American citizen, was raised in Sweden, and has Indian parents. She considers herself a Swedish American of Indian descent. My niece might be considered a Chinese American with Scandinavian heritage. She was a born in China, adopted by Anglo Americans who are mostly of Scandinavian descent, and most of the cultural heritage is Scandinavian. Personally, I like the term American, with nothing else added on.