Married a Chinese national in the United States, do we need to register at the Chinese embassy?

My Chinese spouse told me we need to register our marriage with the Chinese embassy here in the U.S. I could not find any information related to this, only information on getting married in China. I emailed the nearest embassy, and the only information they gave me was this:

If you need your marriage certificate in China, you need do the authentication.
I asked them if there were any additional steps, and they simply informed me they don't know, and instructed me to ask the associated department in China.

Do we really just need to get the marriage certificate authenticated? Do I also need my spouse's Passport?
Thank you in advance.