Legalizing muslim marriage in Korea and U.S.


     My husband and I were married at Masjid in Dusil (without paper).  Now we are trying to legalize it goverment-wise.  We are currently in the process of getting together documents for our marriage book/certificate.  Once we have the certificate, do we just need to go to our embassies and sign?  Are there any other things that we need to do to make sure our muslim marriage is legal in U.S., Korea, and Indonesia?  Thanks in advance for your help:) 

( I know that the certificate would be enough for Indonesia since they're a muslim country, but I'm trying to cover everything in case we want to try to get him into the U.S. so we can be closer to my family when our little one comes.