Scripture is very clear that a believer should not "partner" with and unbeliever - 2 Cor. 6:14 "Do not be yoked together with unbelievers." The term "partner" or "yoked" could refer to any number of relationships (marital, business, etc.) but Paul's primary association was probably ecclesiastically (church) focused. Paul's ultimate concern was that regardless of the situation the unbelievers not lead the believers astray in their teaching of the truth (see 2 Cor. 11:3; 1 Cor. 15:33).
If they are already "partners" (married) then Scripture is also very clear. 1 Cor. 7:12-16 states that the believing spouse must remain with the unbelieving spouse as long as they agree to do so. Divorce is to be avoided because the Christian spouse becomes a channel of God's grace in the marriage relationship. The two are "one flesh" and therefore as God gives His blessing to the believer, the other spouse receives some portion of the blessing. (examples in Scripture are Joseph in Potiphar's house, Gen. 39:5; and Jacob in Laban's house, Gen. 30:27) It is NOT that the unbelieving spouse is now personally justified before God because Romans 14:12 states that "each of us will give an account of himself to God." The ULTIMATE reason why the believing spouse should stay with their unbelieving spouse is that they might come to know Jesus personally by witnessing the example of the believing spouse living out God's love and grace in their personal life (see. 1 Cor. 7:16; 1 Peter 3:1-2).
Bottom line: If you're not married, don't marry an unbeliever. If you're already married to one then stay married and live like Jesus so that your spouse might come to know the Savior and believe in the Good News.
