An interfaith marriage is a marriage between two people of different religions or denominations. In some religions and countries interfaith marriages are forbidden. People in interfaith marriages may suffer intolerance or punishment. These marriages are also a cause of interfaith tensions and violence.
Sharia law places restrictions on interfaith marriage. Muslim men are generally disallowed to marry non-Muslim women (Surah 2:221 ) but an exception is made for the "people of the book" i.e. Jewish or Christian women. Any children must be raised as Muslims. 
Most Muslims say they would not be comfortable if their children were to marry a Christian. 
While polygamy is allowed in Islam, it is a minority practice. It is banned or regulated in some areas and generally not recommended by mainstream Islam. Even though it is illegal, there are an estimated 20,000 polygamous Islamic marriages in the UK. 
To use a partner's own church as marriage venue, there are often regulations on inter-religion and inter-denominational marriage that must be satisfied. Some support groups exist that attempt to facilitate these marriages, such as Interchurch Families.
An inter-denominational marriage that involve a Catholic requires the permission of a priest for the marriage to be recognized by the Catholic Church. Permission usually requires an undertaking from the Catholic partner to raise any children within the Catholic Church and the non-Catholic partner to be aware of this commitment. If the marriage is to take place at a non-Catholic church, separate permission is also needed.  An unrecognized marriage can be later recognized or "convalidated" by the Catholic Church by following certain procedures. The practical implications of having a non-recognized marriage are minimal but it can be spiritually significant to those involved.
Many churches do not marry divorcees or have special procedures in place for this circumstance. Except for a few minor sects, Christian marriages are monogamous.
- Ali Gamal, Egypt: The forbidden love of interfaith romances, BBC, 24 November 2014