Inquiring Mind:
There is a Commandment for Jews not to marry any Gentile, regardless of the religion of that Gentile, even a Noahcide must not marry a Jew. It's a commandment given by G-d, but there are also some obvious rational reasons for that.
1- Jews and Gentiles (supposing the Gentile also believes in the Torah and so keeps the Seven Laws for Gentiles and share the same faith as the Jew) still have different missions in the world and different Commanments. For example, a Gentile is not bound to keep kosher (ha can keep it if he wants, but is not bound to do so), he is forbidden to keep Shabbat, have a Mezuza at his door, etc. etc. On the other hand, the Jew is bound to keep all that Mitzvot. How can a family succeed if man and wife have different laws?
2- Since Hashem forbade intermarriage, such a "marriage" is simply invalid. It would constitute formication. (Gentiles are encouraged not to formicate, and Jews are strictly forbidden to do so). You can easily see that an invalid marriage is not good for any of them.
Now, let's consider the case when the Gentile does not even believe the same as the Jew (that is, a non-Noachide Gentile) and follows another religion. If such were the case, apart from all the difficulties I mentioned above, the couple would have to deal with contradictory beliefs. How can you live with someone who you strongly believe is wrong? If you are a Christian and believe that one must accept Jesus to save one's soul, how can you live with a wife you think is not saved? And how can the Jewess live with you, when believieng in the Oneness of G-d is the most important thing in the world for a Jew, and you believe in the Trinity?