A male relative of mine unfortunately, rachmana l’tzlan, married a non-Jewish woman. She had a huge inheritance from her late father and bought the house they presently live in. Is there any requirement for mezuzot to be put on the doors of their house?
There is a big halachic dispute regarding a house shared by a Jew and non Jew if there is a requirement for mezuzos. I once asked Hagaon Reb Y.S. Elyashiv this very question regarding a mixed couple and he said not to put mezuzos on the door.
Ramo Y:D 286:1, ibid Beis Yosef Bedek Habayis, Prisha, Shach, Taz, Kitzur Shulchan Aruch 19, Maharshal Chullin Chap 11, Hagroh, Beis Meir, Birkey Yosef, Aruch Hashulchon. See also O:CH 14 Mishnah Berurah17. Teshuvos Lev Avrohom 97 & Shov VeRofeh 2:58.