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.
Dear brother in Islam, we commend your pursuit of knowledge and your keenness to seek what is lawful and avoid what is not. We earnestly implore Allah to bless your efforts in this honorable way.
Answering the question you raised, the eminent Muslim scholar, Sheikh `Abdus-Sattar Fathallah As-Sa`eed, professor of Qur'an Exegesis and Qur'anic Sciences at Al-Azhar University, states the following:
"This question can be answered in view of the following three points:
1- There is nothing wrong, as far as Islam is concerned, that a Muslim man marries a Christian woman, but he should stipulate in the marriage contract that any children from the marriage will be Muslims.
2- We hope that the questioner tries hard to call his wife to Islam, and urge her to follow the straight path. In doing so, he will be generously rewarded by Allah Almighty.
3- If all efforts for the couple to reconcile have failed, and divorce becomes inevitable, then the Muslim father is held responsible for the custody of his children and their wellbeing.
Islam has entrusted the man to shoulder the responsibility of the children for fear that the unbelieving mother would guide them to follow her religion. However, if the husband is confident that the mother will not dissuade the children from being Muslims, and he stipulates that in a written contract signed by both parties, then there is nothing wrong in leaving the children in the custody of their mother till they reach the age of seven. After this they should go to their father in order to safeguard their religion."
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