Reference: Silsilah Fataawa Noor ‘alad-Darb – Tape 5
Question: My husband has vowed not to marry so long as I am [married] to him; so is it obligatory upon him to fulfill this vow or not?
Response: This [type of] vow takes on the ruling of an oath; that is because it is [understood that he undertook this vow] from the aspect of a vow taken out of love or anger – as the jurists have referred to it. That is because he either vowed with the intention to only deny himself [and not prohibit himself], so if he wished to marry a woman whilst his wife was still [married to] him, then he is allowed to do that. However, he is required to offer an expiation (kaffaarah yameen) by feeding ten poor and needy people.