Your ONLY priority right now is those two gorg babies.
My ex did similar and left when I was 7 months pregnant so I'm trying to give you the benefit of my own hard won lessons from a similar experience.
No woman is ever as vulnerable as she is in late pregnancy and while her babies are so tiny. However we don't stay vulnerable for long
. Mama Bear will come out quicker than you think & you'll fight for your children to have the best possible future you can acheive for them, whatever he chooses to do 
It takes time to properly think through all the practical implications of staying together versus splitting & right now your babies need the bulk of your emotional & physical energy.
Do not under any circumstances let him push, hassle, or cajole you into anything until you are 100% ready. Right now you need time and space to recover from such a devasting shock and betrayal. Let him sleep in a spare room or on the sofa while you tend to your babies for now.
Only after a good 6 months or so should you make any clear confirmed choices for the future. Once you do make YOUR choice (he's lost any entitlement to a say on whether he should stay or go) should you make your move. Follow through.
One of my reasons for my advice is that I had to return to full-time work when my son was 6 weeks. I still bitterly resent that I couldn't enjoy a nice long maternity break with my baby nearly 8 years on. Let him cover the bills while you enjoy your tiny ones - it's the least he owes you even if you do eventually split 