There were classification laws based on percentage ancestry that determined your racial status. For example, Virginia law said that anyone who was less than 1/8 black was classified as white, more than that was black. Some places employed a 3 tier system that included black, white, and mulatto (or Creole in Louisiana). Mulatto (biracial) people were generally classified as "colored" and faced much of the same discrimination as black people. Depending on the state, the laws about interracial marriage between whites, mulattoes, or blacks would have been different.

In the 20th century, many states imposed the "one-drop rule". This rule specified that if a person had one drop of African blood, i.e. any black African ancestry, that person was legally defined as black. While this was the legal rule, "passing" was a common practice for anyone who appeared white but had some amount of black ancestry.

In contrast to passing, many people who appeared to be white, continued to identify as black because of one drop rules. I attempted to find that name of the NAACP president who, while appearing white, identified as black because of small amounts of black heritage. Unfortunately, the recent Rachel Dolezal case is flooding all of the results when I tried to find this president's name.

Edit: The man was Walter Francis White. He had blond hair and blue eyes, but because of a minority black ancestry, he considered himself a "Negro". Thanks to /u/VitruvianDude for the answer.

so i'm going to attack this from a different angle: multiple races. Remember interracial doesn't just refer to "black and white" but it refers to any cross racial marriage (however you define the different "races" of humanity). I've been rereading Loving v Virginia recently and it struck me that the court's decision here is important. The court showed that historically in Virginia (and thus i assume the other states with these laws) Whites could only marry other whites (see note below about pocahontas) but there was nothing from stopping say blacks and "orientals" (asians) from marrying. These acts thus weren't really about maintaining strong lines between the races as much as maintaining strong lines blocking the white race off from the other races of mankind.

so once you defined if someone was "white" or not, you could figure out what your marriage prospects were.

From Justice Warren's majority opinion.

There is patently no legitimate overriding purpose independent of invidious racial discrimination which justifies this classification. The fact that Virginia prohibits only interracial marriages involving white persons demonstrates that the racial classifications must stand on their own justification, as measures designed to maintain White Supremacy. [n11] We have consistently denied [p12] the constitutionality of measures which restrict the rights of citizens on account of race. There can be no doubt that restricting the freedom to marry solely because of racial classifications violates the central meaning of the Equal Protection Clause.

and here is the footnote 11 cited in the quote

Appellants point out that the State's concern in these statutes, as expressed in the words of the 1924 Act's title, "An Act to Preserve Racial Integrity," extends only to the integrity of the white race. While Virginia prohibits whites from marrying any nonwhite (subject to the exception for the descendants of Pocahontas), Negroes, Orientals, and any other racial class may intermarry without statutory interference. Appellants contend that this distinction renders Virginia's miscegenation statutes arbitrary and unreasonable even assuming the constitutional validity of an official purpose to preserve "racial integrity." We need not reach this contention, because we find the racial classifications in these statutes repugnant to the Fourteenth Amendment, even assuming an even-handed state purpose to protect the "integrity" of all races.

[]

the descendants of Pocahontas

now this may seem like an old timey way of saying "whites and indians" but it is not! Instead it refers to the literal descendants of pocahontas as she and John Rolfe had a son who was born in England before coming back to Virginia and fathering lots of children who became strong parts of the Virginia aristocracy. While the 7/8th white stuff would have been long since established by the time of the 1924 law the inclusion was necessary as an ex post facto justification of such a racial mixing (and thus avoiding the messy problems of classifying a lot of historical virginia elites as nonwhite or biracial).