While I have already touched on this somewhat, I want to consider what scripture says about a marriage in which one spouse is a believer and the other is not. In 1 Corinthians 7:10-17, The Apostle Paul dovetails his teaching on a healthy sex life between a married, believing husband and wife, with the relationship of a married believer and non-believer.
Let me preface this with 2 Corinthians 6:14 which states, "do not be unequally yoked with unbelievers". Now, while the context of this statement has no direct correlation to marriage, it can certainly apply. It is often used in relation to marriage while it's larger context regards any and all relationships. It isn't that we should not associate with unbelievers but that strong bonds or partnerships should not be made with them to include marriage. As we will see, however, this does not permit a believing spouse to initiate divorce with an unbelieving spouse.
Divorce Between Two Believers
He begins with this statement in 1 Corinthians 7:10-11, "To the married I give this charge(not I but the Lord): the wife should not separate from her husband(but if she does, she should remain unmarried or else be reconciled to her husband), and the husband should not divorce his wife." This was contrary to Roman law which would allow "no cause" divorce. Unfortunately America has lined up with the Romans of that day by giving us "no fault" divorce. Between believers in a marriage, biblically speaking, divorce and remarriage with someone else is not really an option, short of the case of adultery. And I believe that forgiveness and at least one second chance should be encouraged, even in that case. God commands us, as believers, to honor our covenant commitment and fight for our marriages. This is not popular however, this teaching came straight from Jesus (Matthew 5:32, 19:9; Mark 10:11-12; Luke 16:18).
Divorce Between A Believer And Unbeliever
In 1 Corinthians 7:12-16, Paul goes on to flesh out the idea that if a husband is married to an unbeliever or a wife is married to an unbeliever that they should not divorce the unbelieving spouse. He states that the unbelieving spouse is sanctified via the believing spouse, as are the children.
Here Paul is suggesting that the overall lifestyle of the family will likely be influenced in a more holy fashion by the presence of the believing spouse, NOT that the unbelieving spouse will be justified before God(i.e. get to go to heaven) by the believing spouse's faith. However, if you are doing all you can and the unbelieving spouse decides to leave and divorce the believing spouse then the obligation is broken. The believer may, but is not required to, pursue the marriage even further. In the case that they have decided further pursuit will not be beneficial, they are released from their commitment that they may marry again to a believer.
I have spoken, I believe, at length regarding this matter as it has been tied into discussions in other posts. I had not however, actually dealt exclusively with this text and this topic alone. I felt it was important as I believe there are quite a few people out there that may be struggling with just such a scenario.
As always, I want to encourage you to fight the good fight of faith. Pray hard, live out the love of Christ, know the word of God and lean on Jesus. Learn to appreciate the grace of God in your own sinful life and then pray for that same grace to be poured out in the life of your unbelieving spouse. God is the only one who can change their heart and He loves and responds to the prayers of the saints. Albeit not always the way we think He should. Continue to strive to understand satisfaction as found in Christ when it is not found anywhere else. God is most glorified in us when we are most satisfied in Him. Miracles can and have happened in marriages such as the one's discussed. As I have said before, God is a fan of marriage. He wants to see you succeed.
If He releases you by way of allowing the unbelieving spouse to leave, then so be it. Until that time comes, again, fight the good fight of faith for your unbelieving spouse. His answer may still be yes. That is God's will according to the scriptures.