We have the same problem, DS sleeps better on his tummy.
He sleeps for around 2 hours (max) on his back, but at 7 weeks, our paed told us to put him on his belly during his daytime naps to help him with his head that was a little mis-shapen. He slept for around 4-5 hours!

I still freak out about putting him on his tummy for the whole night, so when he wakes around 4-5am for a feed, I then put him on his belly.

Nic