The term I'm familiar with is 'biracial.'
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Sometimes, if one of the two racial backgrounds goes back many generations (i.e., is considered to be more or less homogenous), we might self-identify as
I'm half ~~~~~~.
For instance, someone might want to describe themself as half-Chinese or half-Lithuanian.
I use the latter for myself, because it is true.
Half-American does not work, because American is not a race in this sense.
But a lot of people might wish to refer to themself as (for example) half-Irish , half-Greek , half-Italian , half Japanese , half-Cherokee , etc.
I am talking about people referring to themselves.
For someone to self-identify as half-something is usually a sign that they value that racial or genetic component of their background.
In other words, it is a term that is used positively.
People can also refer to others as half-something, which may or may not be true, and may or may not be intended as a kind statement.
Cautian: We have the term half-breed , which also refers to someone who is considered (rightly or wrongly) to be half something.
It is an offensive term, a racial slur, and pretty much no longer used in today's English.
But it is encased in our popular culture, largely due to cowboy-and-Indian movies , where you might hear the term half-breed used to describe someone who is half-American Indian and half-something else.
In the 1970s television show, Kung Fu , the main character is half-Chinese and half-Caucasian American.
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Here we say mixed ethnicity.
The term mixed race,
although implied, would not be used officially in a multicultural society since it might offend.
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You can use the term Eurasian for someone who is half Asian, half European.
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The term dual heritage is also used in public services to describe someone with two ethnicities.
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My mother is an American and my father is a Chinese, is there a term for people with two racial backgrounds in English?  Update: Is "halfer" a good word for it? Is it kinda derogatory?
How to call people with two racial backgrounds in English?
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Mixed ethnicity, biracial, dual heritage can be used to describe someone with two racial backgrounds. The term  Eurasian can be used  for someone who is half Asian, half European. Biracial and mixed ethnicity can work, as well as dual heritage. Eurasian is one example.
Biracial and mixed ethnicity can work. Dual heritage can be used, Eurasian is another example.