My notes says that "according to many, there is no Biblical prohibition against cohabiting with a non-Jew." Is this correct? Is it possible that Biblically, God could be okay for a Jew to be married to his wife and be completely promiscuous with non-Jewish women?
We have to understand that even though a certain act is not prohibited by an explicit prohibition ("Lo Ta'aseh"), that does not mean that G-d condones such an act. Rather, such an act is still condemned and the one who performs such an act is not considered to be an upright, moral individual, but the Torah did not find it necessary to prohibit it, perhaps because it is (or at least, was ) so obvious to all that such an act is revolting.