1. You do a consular report of birth abroad for the child at US consulate near you. Get CBRA and US Passport.
a. Husband will need to prove 5 years of U.S. residence during his life - 2 of which must have happened after age 14 -- And prove his US Citizenship as well.
b. Your husbands signature will have to be part of the filing. Ask embassy if notarizing his sig is acceptable or whether he has to fly to the consulate to sign it.
c. Husband will also have to jointly authorize the child to issue the passport.
d. If child born out of wedlock, embassy can demand DNA paternity test at their discretion but generally do not when couple is married and birth certificate correlates parents.
e. If all goes well, the U.S. Passport & CRBA issued there within 2 weeks. Child must personally appear before the consular officer.
2. As for you - I am presuming you are an interview waiver candidate who came in on K-1 or K-3 and then traveled on the EAD/AP combo card back out again. . Again, as long as your AP remains valid and you did not accrue a 3 or 10 year bar for overstaying on exit (ignoring Arrabally decision here which might override that ) then you would likely be paroled in. If for some reason you are approved or denied for your CPR/LPR while outside, I'm not sure exactly how it would play out.
