I am the product of a mixture similar to that. While there was a push from my mom to acknowledge african history, by the time my sister and I were 10, we both rejected it, and my mother seemed a little saddened by that but she accepted it.
My mom doesn't say "ax" (ask) or boff (both), so we never picked up that accent. The majority of her siblings and other family members do though.
We both look 100% Malay or SEA, which is the race of our father. We both have straight hair and Malay appearances. That has determined so much of our lives I feel. Since we don't look like we have an ounce of SSA, but genetically we are around 30% Sub-Sarahan African. Thats more than Soledad O'brian. I find it hard to believe to this day.
Between me and her, I am the only one that has somewhat embraced black culture. I liked hip-hop and I also always watched black movies. She has 100% rejected everything black, and has little to no contact with our Black family. I also have 1 black friend, and she has no black friends and has never had a black friend or boyfriend in her life. She is currently married to white man who isn't the biggest fan of Liberal politics, and has said insulting things about the NAACP and other black institutions.
I read and hear stories about mixed black people, and I have never once heard a story that was similar to the lives of my Sister and I. We live and operate in a world that is not within the realm of black people or the black community, and somehow we are 30% black. Never once have we been acknowledged as being black people by anyone (including blacks), and honestly, we have never once identified as being black. Sure, we may say that we are mixed (I rarely say that I am mixed unless I feel it benefits me), but our circle of friends, associates and lovers seem to say that we are not african Americans.