Answer
Wa `alaykum as-Salamu wa Rahmatullahi wa Barakatuh.
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.
In this fatwa:
You have to bear in mind that having a girlfriend is not the manner of a Muslim. It is forbidden for a male Muslim to have a girlfriend, and likewise it is forbidden for a female Muslim to have a boyfriend. As for the permissibility of marrying a woman from the People of the Book, it cannot be generalized.
Focusing more on your question, Sheikh Ahmad Kutty, a senior lecturer and an Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states,
Although religiously speaking, it is permitted for Muslims to marry women belonging to the People of the Book (i.e., the Christians and Jews), this permission cannot be generalized. Even during the time of the second Caliph, `Umar ibn al-Khattab, we read that he forbade some of the eminent companions of the Prophet from marrying women of the People of the Book (Ahlul-Kitab). He asked those companions, “If everyone were to make use of this permission, who would marry Muslim girls?”
For Caliph `Umar at that time, it was only a question of Muslim women remaining unmarried. For us today, there are other complications arising out of such marriages.
Our experience with such marriages in North America (and other Western countries) compels us to conclude that after the initial phase of the honey-moon, often intractable problems may arise when the couple settles down to start living together and establishing a family.
Such nagging issues include: Which religious festivals to celebrate; what type of food should be eaten, how are the children to be brought up?
These are issues that pose serious challenges in marriage. It is not unusual to see that sometimes the father is even prevented from praying in front of his own children, while they are taken to church on a weekly basis. It is therefore not at all surprising when we see that the vast majority of such marriages end up in court.
The heavy toll of such marriages on the children cannot be over emphasized. The absence of a unified spiritual vision is bound to produce a generation of confused people who are totally deprived of any religious vision or ideals. Thus, in the final analysis, such marriages cost dearly spiritually, financially and emotionally.
If you still wish to proceed with this marriage, you must know that you are taking a big risk. Nobody can stop you from doing it, but you alone are responsible for your action.
Last but not least, your parents have every right to advise you against it. After all, they have brought you up and sacrificed for you, and so it is not wrong if they offer you the best advice they can.
Allah Almighty knows best.