The scholars discuss this issue in detail in the "Principles of Jurisprudence". We can say here that when the Quran and Sunnah does not directly provide a solution, the jurists still refer to the verses of the Holy Book and the narrations of the Prophet and the Imams (peace be upon them) to get the general guidance in such situations in order to arrive at the practical duty in them. Some narrations can be used to reveal basic principles denoting the practical duty of the individual in certain cases, like "everything is permissible unless one knows that it is prohibited".
It is permissible to marry a Muslim, a Christian or a Jewish woman temporarily. Marrying a woman who does not believe in one of these three religions is not permissible. It is necessary to make sure that she does believe in one of these religions before marrying her.