I believe there is a misunderstanding here. Some posters are talking about being proud of being white, or white culture, white heritage, etc. There is no such thing as a homogeneous "white heritage", as others have pointed out. Rather, we have an American model or ideal, which was constructed out of bits and pieces of ethnicities that came to this country, and that were "white". Think of the ads that you would see back in the forties and fifties, where the all-American family was depicted as a WASP family (did you ever see the film "Back to the future"? Parts of it are a not-so-tongue-in-cheek joke about that ideal). Not one person orchestrated that. Think of it more as an organic process, whereby people who are the targets of this cultural construct then go on to reproduce and reinforce that model. That is to say, the construction of that ideal American culture or family deliberately excluded the contributions of non-white cultures. Those non-whites still contributed to the amalgam that is the U.S., because culture has a life of its own, and although it can be shaped or channeled in a certain direction, it's always cross-pollinated, it's always hybrid, specially in such a large and diverse country like ours. Now, before anyone gets all worked up, this is not a reflection on anyone who is alive today, I am not accusing anyone of being racist or anything of the sort. Instead, it's an observation of what has happened over many generations.
Now, the fact that it is constructed does not mean that it's artificial. All cultural ideals are constructed. The difference here is that the American ideal was constructed not out of a more or less homogeneous local culture that had evolved slowly over time, with limited external influence, but rather from things that everyone brought to the table, mixed with the experiences that were uniquely American, like the Western frontier, the early settlers, etc. (some of which are also constructs, by the way). And the people who were in a position to shape and mold that ideal happened to be white, so they looked for things that other whites did and included them in that construction. If you every go to Italy, Sweden, Spain, France, Germany, etc., you will find that their cultures differ significantly from one to the other, and if you go to Russia, Bulgaria, Romania, or some other Eastern European country, they might be even more different. Or, if you want an extreme example, think of Northern Iran, where many of the original Indo-Europeans came from. If there were such a thing as white culture, all those countries and/or regions would be the same or extremely similar. (In point of fact, a very, very interesting area of anthropological research is the tremendous diversity that exists among white Americans).
Now, to address the OP's point more directly, I think that we all have a heritage, we all have a cultural background. What happens is that it feels like you don't because you are part of the dominant model. People who are not part of it, like your husband, react in at least three possible ways: they assimilate completely into the dominant model (in this case, the white construction that I talked about); they react against it by being overly proud of their particular ethnicity or cultural/national origin; they integrate into the dominant environment, make it theirs, contribute to it, but keep the distinctive parts of their ethnicity, so that they can claim an identity that is both general and unique at the same time.
My advice would be to be proud of who you are. Not as mechanism to feel superior to anyone else or any other culture, but rather as a testament to the dedication of your family and to the positive aspects of your community. I am sure that you have more specific cultural traits than you think you do. As several posters have said, you are a product of your environment, of your family, and you carry those things with you. Sure, go look for your ancestry, and that might explain some of the habits your family or your community has. But overall, I am always somewhat puzzled and amused by people who say that they are X because their great great grandfather was X. That is not how culture works. If it were genetic or transmitted by blood alone, then it wouldn't be "culture".