Paperwork to prove the birth of a baby in the U.S.

My husband is working in Germany, and I'm currently in the US with our new baby and waiting for the baby's passport to join my husband in Berlin. He needs some kind of paperwork for the tax authorities and for insurance purposes showing that he has a child now, so that he can sign us onto his insurance and have less taxes subtracted from his paycheck. Question: would he need anything besides a US birth certificate with an apostille stamp on it, and does it need to be accompanied by a somehow official (notarized? performed by a licensed translator? authorized by a German consulate here? what?) translation?

I don't know anything about the paperwork you might need, I'm afraid. I just wanted to say congratulations on the birth of your baby!