If you are a U.S. citizen married to an immigrant you will need to have documents that prove your citizenship. These include a U.S. passport, a birth certificate issued by the civil registrar if you were born in the country, a naturalization certificate issued by the USCIS office if you acquired citizenship through naturalization, or the original certificate of citizenship or "Report of Birth Abroad of a U.S. Citizen" issued by the U.S. embassy in the country you were born in.
An original certificate of marriage shows that both you and your spouse entered into a legal union. It is proof that the marriage was valid in the place and time it was performed. The validity if your marriage depends on the laws of the place that you were married in, be it the United States or elsewhere. You will also need a proof of termination of all previous marriages if you were previously divorced.
Other than the certificate of marriage, you need evidence of a bona fide marriage. This is means that your marriage was not for the purpose of immigration only. Evidentiary documents of joint home ownership or lease, joint bank and credit accounts, joint tax returns or health and auto insurance can be used. You may also require a statement or affidavit from a third party such as a priest affirming that your marriage is indeed bona fide.
If you have children, their birth certificates, issued by the civil registrar in the United States, are essential proof that you and your spouse are in a legal union. If the children were born outside the country it is important to obtain appropriate documents such as "Report of Birth Abroad of a U.S. Citizen."