Officially, for it to be a Jewish wedding, both parties need to be Jewish. My parents were married by a reform rabbi in a reform synagog and my mom needed to convert before he would do the ceremony.
I mean, how they conduct their household is up to them, but for it to be generally recognized in the faith writ large he'd need to convert officially and do that whole course of study and have a full fledged Jewish ceremony. I'm not sure if they care enough for that whole dog and pony show.
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