I am from the privileged half of a similarly divided couple. In fact, while I went to prep school and a very expensive top tier university my partner went to community college. He doesn't have a 4 year degree, or anything like that. And there is a clear class divide between our families that manifests in several obvious ways.
But we talk about it ALL THE TIME. I never hold back on talking about my life because it might make him feel bad, and I want to know more about his so I can understand him better. There are just huge differences in how we were raised and in how we think about the future, and we have to talk about it.
The differences between our lives and our experiences are part of what make our relationship work. And talking about it brings us closer together and lets us talk about how we want our lives to be in an ideal world. We never sit down and go "Okay, lets talk about how you having a fewyears where your dad hunted venison so you could eat makes you different from me because I've been to disney world like 9 times." But we do talk about those things, and we both listen and realize that it is not a judgement on us. We are both a product of our upbringings and we love eachother as we are.
One thing I would say is that knowing his family and friends has given me SO much perspective. They are almost all in construction or some other trade, and seeing how they struggle and how hard they work has made me very very very aware of my privilege. That is hard sometimes, for me.
I guess I"m just saying, it is part of both of you, and you should talk about it. All the time. And realize that one person's experience isn't a judgement of another's it is just a difference that makes you different.
(That said I do have a brother in law who gets... uhhh. emo... every time an event is not about him. How does he do at other people's birthday parties? If the answer is not so good, it might be a different issue.)