What is your definition of "open marriage"?
I understand it to be when a man and woman are legally married to each other, but free to have sexual relationships with other people.
But since they are married, the terms "husband" and "wife" still apply.
Maybe you mean what we call a "common law" marriage? That's where people live together as husband and wife without being legally married. In some US states (following the English common law), living with someone for a certain number of years can automatically convert a relationship into a legal marriage.
Or do you just mean when two people live together? There is no standard term for that.
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