Just go to your husband's GP and tell them you want to register as a new patient. They should accept you - they'll give you something to fill out. My GP submitted my info to NHS for me and we got our cards in the post months later - but it's no big deal because no one ever asks to see the card or what the number is.
I took my passport to show my settlement visa, but nobody wanted to see it. Just said, "If you're living here, you're eligible. Fill out the paperwork and bring it back in."
But I would take it just in case. Can't hurt to have it on you.
Oh - and I had all my records regarding birth control with me from the US. I had been getting Depo shots at Planned Parenthood since Jan 2001 and wanted to make sure I was able to continue them without any lapse. Was a good thing I brought them, because they still administer the shots in the butt - I'd been getting them in my arms and they continued with that since I had my records.