One of mine was cs, and was not separated from me.
The other was not cs, but I was told that if he was I would be in recovery for a few hrs without him!! (I think it was that moment I decided I was vbacing - no matter what!)
This was 2 different hospitals, so I guess each one has its own policies and then depends on the day whats happening and whos on etc.

Im not sure what to suggest to your DH, but let him know your anxious about it and ask him for his suggestions of what might work for you all?
We kept our cs time and day a secret... Im not sure of how doing the big annoucement at the hospital works in reality. I dont know anyone who has done it that way.