Hey.
I'm a military wife and I recently received my permanent residence through marriage. Yes, for military spouses, it can be easier to adjust.
To obtain your husband's birth certificate, you can find out where he was born and call the office of vital records there. That's how we got my husband's birth certificate.
I'm don't know if you know (because some people tend to think it's impossible), but you can be enrolled in DEERS, receive free healthcare, dental, get a dependant ID, etc. Also, make sure your husband lets the military know that he is married ASAP so he he can begin receiving BAH and BAS.
Oh, and you can go to immigrate2us.net for more info.
Good luck! =)