I was meditating and thinking on this passage of Scripture some more even after I got responses here and I came to this thought...Could someone please tell me if this makes sense or if I am way off base?
I command the married--not I, but the Lord--a wife is not to leave her husband. But if she does leave, she must remain unmarried or be reconciled to her husband--and a husband is not to leave his wife. But to the rest I, not the Lord, say: If any brother has an unbelieving wife, and she is willing to live with him, he must not leave her. Also, if any woman has an unbelieving husband, and he is willing to live with her, she must not leave her husband. For the unbelieving husband is sanctified by the wife, and the unbelieving wife is sanctified by the Christian husband. Otherwise your children would be unclean, but now they are holy. (1 Corinthians 7:10-14 HCSB)
I found a connection between that passage that I've been struggling with and this one from James:
What good is it, my brothers, if someone says he has faith, but does not have works? Can his faith save him? If a brother or sister is without clothes and lacks daily food, and one of you says to them, "Go in peace, keep warm, and eat well," but you don't give them what the body needs, what good is it? In the same way faith, if it doesn't have works, is dead by itself. But someone will say, "You have faith, and I have works." Show me your faith without works, and I will show you faith from my works. You believe that God is one; you do well. The demons also believe--and they shudder. Foolish man! Are you willing to learn that faith without works is useless? Wasn't Abraham our father justified by works when he offered Isaac his son on the altar? You see that faith was active together with his works, and by works, faith was perfected. So the Scripture was fulfilled that says, Abraham believed God, and it was credited to him for righteousness, and he was called God's friend. You see that a man is justified by works and not by faith alone. And in the same way, wasn't Rahab the prostitute also justified by works when she received the messengers and sent them out by a different route? For just as the body without the spirit is dead, so also faith without works is dead. (James 2:14-26 HCSB)
My connection is that the believing wife or husband sanctify the unbelieving partner and their children by living such a Godly life that the unbeliever has no choice but to make a decision in favor of salvation in Christ. And that holds true for the children as well. They will see their parents living such Godly lives that eventually they will come to a saving knowledge of Jesus. This way, the faith can pass to the next generation. And it was by the works of the parents, indrectly, that led to their children being saved and thereby keeping the faith alive for another generation. Please let me know if I am wrong in this notion.