How as a American marrying a German citizen can I get a German passport?

Yes, in Mexico and most other Latin American countries.

Not in the USA, he has to live in that country first for 3-5 years and then apply for this citizenship.

I wish it was easier, going through the application myself at this time.

Die gute Nachricht: man braucht seine deutsche Staatsbuergerschaft nicht abgeben, um Amerikaner zu werden.

More Info I found here, I hope this will help you:

http://www.usimmigrationsupport.org/citizenship_application.html

Good luck!