Good that we have same status during the time I gave birth to our daughter 16months ago. These are the things that we did during those times:

1. Have with you always complete document both for you and your husband (authenticated Marriage Certificate)
2. Go to the NHA (beside Lulu Supermarket-infront of Women's Hospital) to register your baby (the hospital card)
3. Then NHA will advice you to go to CID office (Salwa Road-going Abu Samra) to give some other documents.
4. Go to the 1st floor right wing ask for Birth Registration Section (take along with you one Filipino friend or relative who is willing to leave original passport as a witness and for verification)They will ask you to come back after a week or two

Remember that Government Offices here serves at 7am till 11am only. And you have only 6 weeks after giving birth to register your baby or you will pay penalty. Btw, no need to take along your baby with you. Your husband can do all the things.

GOODLUCK...