When my baby was tiny he did this too. I was afraid to leave him on his tummy to sleep, as they have to get less air in the lungs if they have the whole weight of their body on their lungs. I put him to sleep in the big one piece pajamas with footies that zip up in front, so there was no blanket to suffocate with. The little baby blankets that we all have so many of... I rolled one up tight and put in longways down the front of his pajamas. This made it impossible to sleep on his stomach. In fact, he learned to sleep on his side, and it looked like he was hugging the big roll in his pajamas. So he could move around, and change positions without me, and not suffocate, and not end up stuck on his belly. He looked silly, but he was safe. Sometimes, when his diaper soaked through, the recieving blanket roll was wet too, so we kept extras rolled up blankets ready by the changing table. Give it a try, it really helped, and we all got more sleep.
Good luck.