Assuming you mean Black & White, the usual answer is Black, but to my knowledge there's no legal precedent, Regardless of the child's skin pigmentation, once there is mixed lineage in a child's heritage it is thereafter possible that a subsequent child of the racially mixed child could exhibit traits of one or the other parent, (or even grandparent) i.e., a white child with features normally associated with Blacks (nose, mouth, hair) or a Black child with features more predominate in whites, i.e., blonde hair, blue eyes, etc. The further generations back, the less likely this is to occur. Wikipedia is likely a better source for information that you will find helpful. Google "I passed for White" (a 1960 movie). In the results look up "passing racial identity" There's a lot of good info there. Legally there is no distinction.
Well I'de say the nationality would be where ever the child grew up & the ethnicity is mixed race! Which of course is great & makes it more interesting! Sorry if this is an answer you didn't really want!