If you were permanently employed with an American registered airline in the USA you would need a "green" card [residency] and a Social Security card, because you'd be paying Social Security Tax, and Medi Care Tax and Income witholding tax; it wouldn't matter if you lived next door in the Bahamas or in Sweden. You will be subject to USA taxes.
If you work for a Part-121 Air Carrier then you could jump seat internationally with another Part 121 carrier if your carrier had a reciprocal agreement as such.