Christian-Muslim marriages do occur, but the religious rules are not identical across Islam or Christianity. Couples need to distinguish civil legality from religious recognition and to discuss worship, children, family expectations, and marriage contracts before the wedding.

Islamic perspectives
Classical Islamic jurisprudence generally permits a Muslim man to marry a chaste Christian or Jewish woman, based in part on Qur’an 5:5. Traditional Sunni and Shia legal schools generally do not permit a Muslim woman to marry a non-Muslim man.
Individual Muslims and modern scholars can hold different views, and national family law also varies.
Catholic perspectives
The Catholic Church distinguishes marriage between a Catholic and another baptized Christian from marriage between a Catholic and an unbaptized person. A Catholic-Muslim marriage involves disparity of cult and requires a dispensation for validity in Catholic canon law.
The Catholic party is also asked to preserve the Catholic faith and do what is possible to have children baptized and raised Catholic, while the other party must be informed of that obligation.
Other Christian traditions
Orthodox, Anglican, Protestant, and independent churches have different policies. Some clergy will officiate interfaith marriages under conditions; others will not.
A couple should therefore consult the actual church or denomination rather than assume one Christian rule applies everywhere.
Children and daily life
Questions about children are often more difficult than the wedding itself: baptism, Islamic naming or rites, religious education, holidays, diet, prayer, and extended-family expectations can all matter.
Clear discussion before marriage is more useful than assuming differences will resolve themselves later.
Marriage contract and civil law
Islamic marriage contracts can include conditions, while civil marriage law determines legal rights in the country where the couple lives. These systems may not always align.
A practical approach
Christian-Muslim couples can build committed families, but they should enter marriage with clear knowledge of both religious traditions, civil law, and expectations about children and worship.