In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear questioner, thank you very much for having confidence in us, and we hope our efforts, which are purely for Allah's Sake, meet your expectations.
First, Islam calls upon all people to join hands and to co-operate with each other regardless of their creedal affiliations as long as all work for the betterment of humanity and there is no harm inflicted as a result of such co-operation. Of all the existing religions, Jews and Christians possess a very special status in Islam. Islam allowed the Muslim to marry a woman from among the People of the Book, but a Muslim woman, on the other hand, is NOT permitted to have a non-Muslim man as her husband. The reason is that usually the sons and daughters are ascribed to the father, and Islam’s ruling is that the son or the daughter should follow the true religion; namely Islam. The previous ruling is so inclusive in Islam.
Responding to the question, Sheikh Zoubir Bouchikhi, Imam of the Islamic Society of Greater Houston’s Southeast Mosque, states the following:
“First of all, I would like to stress that Islam is the true religion of Allah (god). Muslims, are enjoined by the teachings of the Qur’an and the Sunnah, to believe in Jesus and Moses as Messengers of Allah, while the Jews and the Christians do not actually believe in Prophet Muhammad (peace and blessings be upon him) as the last and the seal of all Prophets and Messengers of Allah. This may indicate that their beliefs are not complete, and from here came the command of Allah for NOT allowing a Muslim woman to marry a non-Muslim man as man is responsible for his wife and children, and responsibility cannot be given to someone who incomplete in his belief.
I know that this is a little bit hard, but remember that the truth is always bitter for those who are not ready to accept it.
Having said this, I should add here that we are not separated as Muslims, Jews, and Christians by the Books of the same Creator but by the changes that some of the Rabbis and the Priests have made to the true teachings of Moses and Jesus (peace and blessings be upon them all)
Finally, I hope that you study Islam from its main source; the Qur'an and the Sunnah, and not by looking at the behavior of some Muslims. I wish you all the best.”
Moreover, the prominent Saudi scholar Sheikh `Abdul-Rahman Al-Barrak, adds:
“It is not permissible for a Muslim woman to marry a kafir (non-Muslim), whether he is Jewish, Christian or an atheist because the man has authority over his wife, and it is not permissible for a kafir to have authority over a Muslim woman. There are decisive texts from the Qur’an which refer to the prohibition of such marriage. For example, Allah Almighty says, “And give not (your daughters) in marriage to Al Mushrikun (atheists) till they believe (in Allah Alone)” (Al-Baqarah: 221)
And “And never will Allah grant to the disbelievers a way (to triumph) over the believers” (An-Nisaa’: 141)
Finally, we recommend you to read:
Marrying a Non-Muslim Male
Does the Term “Ahlul-Kitab” Still Apply Today?
Muhammad & Jesus: Common Ground
If you have any further questions, please don't hesitate to write back!
May Allah guide you to the straight path, and guide you to that which pleases Him, Amen.