In general, marriages between non-Catholics, of whatever religion, are considered valid, but the situation is not as simple as it sounds because there are two kinds of marriage: natural (ordinary) marriage and supernatural (sacramental) marriage. Supernatural marriages exist only between baptized people, so marriages between two Jews or two Muslims are only natural marriages. Assuming no impediments, marriages between Jews or Muslims would be valid natural marriages. Marriages between two Protestants or two Eastern Orthodox also would be valid, presuming no impediments, but these would be supernatural (sacramental) marriages and thus indissoluble.
When one spouse is a Catholic and the other is a non-Catholic--this is commonly termed a "mixed marriage"--the situation changes. Just as the state has the power to regulate marriages of its citizens by requiring them to get a blood test or to marry in front of a competent authority, so the Church has the right to regulate the marriages of its "citizens."
If one participant is a Catholic who has not left the Church by a formal act, such as by officially joining another church, he must obtain a dispensation for the marriage, which would otherwise be blocked by the mixed-marriage impediment or by the disparity of cult impediment. A Catholic who has not left the Church by a formal act also must obtain a dispensation to be married in front of a non-Catholic minister. If either of these dispensations is not obtained, the marriage will be invalid.