What do you need to do if your spouse is living with another person as husband and wife. Is this Bigamy
No, it is not bigamy, but the crime of adultery. See, Code of Alabama, 1975, section 13A-13-2. Under the Alabama Code, adultery is defined as engaging in sexual intercourse with another person who is not his (her) spouse and lives in cohabitation with that other person when he or that other person is married. Adultery is a Class B misdemeanor.
You should contact the district attorney of the county where you live and ask that this case be prosecuted.