"Yes, She Is!" No, She's Not!" Is birth country the only factor in being "of" a certain people?

As I shared in my last post, my fiance and I recently had a beautiful baby girl. We have found ourselves in a never-ending debate about her culture. My biological father was born and raised in Jamaica and my fiance born and raised in the British Virgin Islands. In my mind, she's about 75% Caribbean. No? Well that's what my fiance says too.
Over the years, I have found myself phasing out American black men from the dating pool and replacing them with Caribbean or African black men (yes there are white Caribbean and Africans). It's just become my personal preference. I love the foods, music, languages, accents, and everything about the Caribbean culture especially. These are things that I greatly want our daughter to be a part of. However, my fiance's feeling that her not being born on a caribbean island makes her 100% American bothers me.

I think it would be a much different story if he [fiance] was completely "Americanized" so to speak but he's not. And please don't let him get around family; it's like, what American accent?! I was not raised with my biological father and I think I have always longed to know this part of myself. Being outcasted by my father's side as a dark-skinned (yeah... they are those light-skinned with "good hair" kind) Yankee and my mothers side as just different all around, has truly affected me. Although I tried to compensate for the void with reggae music, dance halls, plantains cooked every which way, and a former unhealthy obsession with all things Marley, there will always be something missing. My fear is that she will grow up to feel disconnected from her family and that she won't experience the richness of the culture. 

So to all of you bi, tri, and quad(?) cultural people out there, what do you think? Is she? Is she not?