1 Corinthian 7:12-16
12 To the rest I say this (I, not the Lord): If any brother has a wife who is not a believer and she is willing to live with him, he must not divorce her. 13 And if a woman has a husband who is not a believer and he is willing to live with her, she must not divorce him. 14 For the unbelieving husband has been sanctified through his wife, and the unbelieving wife has been sanctified through her believing husband. Otherwise your children would be unclean, but as it is, they are holy.
15 But if the unbeliever leaves, let him do so. A believing man or woman is not bound in such circumstances; God has called us to live in peace. 16 How do you know, wife, whether you will save your husband? Or, how do you know, husband, whether you will save your wife?
In 2 Corinthians 6:14 Paul clearly states that a believer should not marry an unbeliever. “Do not be yoked together with unbelievers. For what do righteousness and wickedness have in common? Or what fellowship can light have with darkness?” However there are often times when a person becomes a believer after marriage and the spouse does not share the newfound faith. This is the situation that Paul addresses in 1 Corinthians 7.
A believer should continue in marriage with an unbeliever as long as the unbeliever desires to remain married. A Christian should not initiate a divorce. Even though there may be difficult circumstances, a Christian is still a witness to their spouse as long as they are married.
Likewise, the children of the family are sanctified by the believing parent. This does not mean that they are saved because they have a parent who is a Christian. Instead it means that they are exposed to Christianity and have a greater chance of becoming a Christian because of the influence of the parent.
If the unbelieving spouse wants a divorce, the Christian should let them go. This does not mean that everything possible shouldn’t be done to first save the marriage. The reconciliation of a husband and wife is always the first goal.
After every resource has been used to save a marriage and an unbelieving spouse still wants to leave, the Christian should let them leave without the guilt of divorce upon them. They have no control over the decision of an unbelieving spouse. Likewise, they should not remain in the marriage because of the chance to witness to their spouse. While this was a viable reason when the spouse wanted to stay, it is not a reason to maintain the marriage. As Paul says, there is no way to know if a person will lead their spouse to the Lord.
As to whether a believing spouse can and should get remarried, this is a much more difficult question that will be discussed in the article, “Should I Get Remarried?“