Well, sure, you can have 2 birthday celebrations. When people become adults, a group celebration often doesn't take place on the exact day, because people prefer weekend nights.
But if he's like this with holidays, too, you might have a separate problem. Why does he always get his way? For that matter, why doesn't he like family involvement? My husband and I spent our first Christmas together, but this was something we both wanted. We knew after that, we'd be spending it with families, and this too was something we both wanted.
Marriage is all about compromise (you give a little to get a little). If you're the one doing all the "giving", this isn't fair and you'll start resenting him. If that's happening, you need to talk to him about it.