Depends whether you're the subject or object of the sentence. If you're the object, you'd say "Give it to my husband and me." If you're the object, you'd say "My husband and I gave it away." The easy test is to remove the part of the sentence that isn't I/me - you wouldn't say "Give it to I," you'd say "Give it to me." But you wouldn't say "Me gave it away," you'd say "I gave it away."
I know which to use when, but I think 'and me' always sounds wrong. I think I must have been taught it incorrectly as a child (that you always say I no matter what?!) so I feel very self conscious when I use 'me' (correctly) as I feel many other people of my generation will judge me for it.
^^ not sure that makes sense outside of my head! I need coffee.