To this situation, many quote II Cor. 6:14 - "Do not be unequally yoked with unbelievers. For what partnership has righteousness with lawlessness? Or what fellowship has light with darkness?" (ESV)
Rather, as he warms to his topic it becomes clear by verse 16 that the subject is religious idolatry, which was very common in the city of Corinth. Let's face it, the city was so packed with temples and altars to all kinds of gods that Paul found a shrine dedicated "To An Unknown God." (Acts 17:23) You know, just in case they missed one. So unless your spouse is into worshiping a pagan god this verse really doesn't apply to you.
For those Christians who are married to a spouse who is not, how are you to respond to your situation? Fortunately, I Cor. 7:12-16 speaks to this.
Paul says if a brother (in Christ) has an unbelieving wife or a Christian woman has an unbelieving husband, if their spouse is perfectly content to continue living with them, then they should do so. It's not grounds for divorce.
However, the unbelieving husband is sanctified, or set apart and made holy, by the believing wife. And the unbelieving wife is sanctified by the believing husband. This does not grant them automatic salvation. But God has his eye on them for your sake.
Verse 15 reassures you that, if the unbelieving spouse chooses to leave, you're not obligated to go to herculean lengths to maintain the marriage. God has called us to peace. (I love that!) Hanging on to them in hopes that your love and prayers will one day result in their salvation is unrealistic and doesn't take into account that this is a separate human being who is responsible for their own decisions.
Maybe your efforts will result in their salvation. Maybe they will continue to refuse God. This is not for you to know. Although divorce is clearly not the standard among Christians, we are not in bondage in such cases.
God has called us to live in peace.