The U.S. Embassy in Beirut explains this: All marriages in Lebanon are performed by a religious authority and are registered in the husband's jurisdiction of birth. Those wishing to have a civil marriage must marry outside the country. In cases of interfaith relationships, either partner can convert to the faith of the other for the purpose of marriage.
So that's okay, right? I wonder if couples flip a coin to see who gives up their religion.
I figure that Lebanon isn't going to have same-sex weddings for a long, long time, but you have to start somewhere, right?