I think the title of the question pretty much says it all. Furthermore, since they are living together, in the same home, can the Gentile spouse eat the chametz in presence of the the other spouse, or only when (s)he is not there and / or in another room?
While I don't see a problem with selling to the Gentile, per se, I am wondering if there may be a problem in this case, since the two live together, share the same kitchen, and it is fairly easy for the Jewish spouse to see his / her chametz during the week, esp. if his spouse is eating in front of him / her.