I’m a foreigner, if I marry a US citizen, after I get the green card, can we live in two separate states due to our jobs?
In order to be able to apply for naturalization in a period of three years instead of the normal five years period based on being the spouse of a US Citizen, the person must present evidence that he or she is married to the citizen spouse at the time of the naturalization interview.
Evidence is required to prove the fact of marriage and that the marriage is a bona fide marriage, because the law provides for a shorter period for spouses of US Citizens than for non-spouses of US Citizens, so, existence of marriage and a bona fide marriage will be investigated by the adjudicator.
The fact that your husband and you live in separate states because of each others work does not constitute a valid ground for an adjudicator to deny the existence of the marriage or the bona fide of the same. The important question is whether you and your husband act in front of each other and in front of the community at large as husband and wife. There is sufficient case law that discusses situations like the one you present in your question, and valid marriages for purposes of acquiring citizenship after three years have been found to exist even if the spouses live apart for considerable periods of time – as long as they can introduce other evidence that shows that they act in front of each other as husband and wife.
Calls, emails, vacations, short trips, bank transfers, common bills, joint accounts etc will prove that is a bona fide marriage even though the parties are living apart for professional reasons.