A Jew is forbidden from marrying a non-Jew
Intermarriage
It is forbidden for a Jew to marry a non-Jew. This sin is punishable by karet.8 In addition, the Talmud says9 that a man who commits this sin loses the spiritual protection of the brit milah—the circumcision, the covenant of Abraham.
Even if a Jew and a non-Jew have a wedding ceremony, the marriage is deemed invalid under Jewish Law.10 In the case when a child is born, he or she will not be considered Jewish if the mother is a non-Jew.11
SOURCE
Permitted Marriages - Parshat Acharei - Mitzvahs & Traditions
Although it does seem some non-torah observant Jews allow Jewish men to marry Gentile women
When I was Catholic in the 1940s it was forbidden for a catholic to marry a non Catholic even if they were another Christian denomination. Catholics back then only considered a catholic church marriage to be a valid marriage and for that both had to be catholic. In Catholicism and orthodoxy marriage is a religious sacrament and only members of the faith can participate.
Even today you will find most Christians forbid marriage with a non-Christian
The Bible is actually much more direct about marrying unbelievers than has been indicated to this point. The Old Testament specifically forbids God's people from marrying "foreign wives":
"Now therefore, make confession to the LORD God of your fathers and do His will; and separate yourselves from the peoples of the land and from the foreign wives." (Ezra 10:11)
The Old Testament contains other verses that prohibit marrying unbelievers, including examples of those who broke the command and were led astray by their wives (e.g., Solomon in his later years).17 In the New Testament, Paul specifically says that a woman may marry whomever she wishes, but "only in the Lord," clearly referring to those who are followers of the Lord Jesus Christ.18 So, the New Testament makes it clear that believers are only to marry fellow believers.
Dating a non-Christian?
Although dating of Christians and non-Christians is not specifically handled in the Bible, it is clear that such an action is asking for trouble. An unbeliever who practices Christian-like morality is going to be attractive to a Christian. However, the chances that such a person will become a Christian, allowing the Christian to marry him/her is statistically remote. "Missionary dating" often results in years of conflict and usually ends in broken hearts.
SOURCE
http://www.godandscience.org/
Muslims, Jews and Christianity all discourage different faith marriage. Muslims are just a little more willing to allow it in some circumstances.
On a personal basis I discourage all mixed faith marriages and think they all are a potential disaster.
Felt that way when I was Catholic. Felt that way when I was Protestant felt that way when I was Atheist and still feel that way as a Muslim