http://revach.net/article.php?id=4503

Section: Halacha   Category: Tshuvos
Rav Moshe Shternbuch: Mezuza On The Home Of A Mixed Married Couple
Someone offered a mezuza to a Jewish man living with a non-Jewish woman.  The man agreed to pay for it and hang it up on his door.  Rav Moshe Shternbuch was asked (3:327) if it was worthwhile to help him at least keep this one mitzva, despite his grave situation.

Rav Shternbuch answered that a Jew who lives with a non-Jew has a Din of a Meshumad, someone who converted to another religion.  A Meshumad is not even entitled to be buried in a Jewish cemetery, and neither is someone who lives with a non-Jew.  This is worse than any other aveira in the Torah.  He is not merely Oveid Avodah Zara he is a Meshumad.

A mezuza says Rav Shternbuch, is sign of Ol Malchus Shamayim.  A Meshumad cannot have such a sign on his door.  Even a Michalel Shabbos Bifarhesia may, and should, have a Mezuza because he can justify in his own mind a belief in Hashem.  However this man wants live with a non-Jew, yet show that this is a fine arrangement for a kosher Jewish home.

Technically speaking, says Rav Shternbuch, the house is not even Chayav in Mezuza since in secular law the women is part owner in the assets, it becomes a house that belongs to both a Jew and non-Jew in partnership, which is not chayav in mezuza according to most Poskim.

The bottom line says Rav Shternbuch is that not only are you not obligated to assist him with his mezuza, but it is forbidden.  It is our obligation to ostracize him until he divorces her and returns B'tshuva Sheleima.

Important Note: We bring this tshuvah as a starting point for discussion and not to convey any halacha.  We try to convey the Tshuva to the best of our ability. We admit that our understanding may not be accurate. One should learn the tshuva to verify the accuracy of our interpretation.  Please understand that this Tshuva may not be the final word on this topic. One should consult a Rav before drawing any conclusions.