I guess it is an affair, but maybe just not cheating since it is not a secret.
An affair does not have to be secret to be cheating. If your spouse is being unfaithful, openly or not, then they are betraying the vows of the M. They're cheating both the M and their marriage partner of what they made a covenant, before God and witnesses, to uphold.
In more secular terms, they have breached a contract and cheated their contract partner.
