Why not? If both families can see past religion it will definitely work. The big question would be what kind of ceremony will they have?
The easiest of course would be to have a secular wedding yet have elements of both culture interwoven. They will be legally married. Within their faith though, there might be questions about validity depending on whether the man or woman is Jewish or Muslim.
An interfaith couple planning a Jewish-style wedding, however, faces a number of obstacles, the first and foremost being that not all rabbis will not officiate at interfaith ceremonies. A Jewish wedding is by definition sectarian--its pivotal sentence requires the groom to marry the bride "according to the laws of Moses and Israel." If one partner is not Jewish, those laws don't apply, and the marriage is invalid in the eyes of halakhah [Jewish law]. Yet even if a rabbi explains this rationale clearly and sensitively, it is very hard for a couple not to feel a sense of rejection.
Muslim Wedding (from Wikipedia)
In practice, many Arab countries allowed interfaith marriage to Christian or Jewish women but not to non-Muslim men. Turkey allows marriages to non-Muslim men through secular laws. In Malaysia a non-Muslim must convert to Islam in order to marry a Muslim. The offspring of such unions are automatically Muslims and all Malaysian Muslims are legally prohibited from leaving Islam (Riddah).