I had the same problem before, but nowadays I can get somewhat more comfortable on my back, but still not as comfortable as on my side or front. However, what I did was just practicing to fall asleep on my back. Listening to some music, and concentrating on it, when going to sleep helps forgetting about your body and the uncomfortable feeling of lying on your back. Soon you should just fall asleep.

I think it's just about getting used to lying on your back and being able to find a comfortable position. And that, I think, comes only with practice.