I also had emergency c on my 1st. I was told the husband is not allowed because it's an emergency and they need to be able to devote all their energy to making sure you and baby are okay. I'm kinda glad I was unconscious and DH wasn't in there for DD1 b/c she wasn't breathing and they had to do CPR to keep her alive until she was intubated and rushed to the NICU.
I would do the following:
1) Discuss with DH carefully what you want to happen so he can advocate for you.
2) Ask for baby and DH to be there when you wake up. If baby is healthy I see no reason they can't do this.
3) if you don't want everyone to meet baby before you, check the option on your forms that it is not ok to release either your names/locations or the babys to anyone who calls, and let DH know you want the three of you to be alone until you get to meet your baby.