In I Corinthians 7:12-14, it doesn't mean a Christian marrying an unbeliever. You need to see the background and the circumstances Paul wrote this letter. Actually the problem in Corinth is that after marriage a husband or wife accepted Christ. Because of the desire to serve Christ, the believing wife or husband thought they ought to divorce their unbelieving spouse and marry a believer. To this problem, Paul wrote an answer, but it doesn't mean Christians can marry unbelievers. This is my opinion regarding the above passage. There is something conflicting. Please correct me whether it is right or wrong.
The problem is that you are reading into this passage things that are not stated. Just as it is wrong to ignore something God has said, it is equally wrong to modify what He said by adding in more than what He told us.
"But to the rest I, not the Lord, say: If any brother has a wife who does not believe, and she is willing to live with him, let him not divorce her. And a woman who has a husband who does not believe, if he is willing to live with her, let her not divorce him. For the unbelieving husband is sanctified by the wife, and the unbelieving wife is sanctified by the husband; otherwise your children would be unclean, but now they are holy. But if the unbeliever departs, let him depart; a brother or a sister is not under bondage in such cases. But God has called us to peace. For how do you know, O wife, whether you will save your husband? Or how do you know, O husband, whether you will save your wife?" (I Corinthians 7:12-16).
You assume that the two non-believers married and then one became a Christian. However, read the passage again carefully. Where in this passage does it say this? It would cover the situation, but all that is stated is that a man or woman has a non-believing spouse. It makes no qualifications as to how the situation arose. Because of this, it is wrong to add that qualification in.
The statements Paul makes applies to a believer married to an unbeliever regardless of how the situation came about. It would cover a Christian marrying a non-Christian. It would cover two Christians marrying and then one falling away into sin. See "Marriage" for a detailed study on I Corinthians 7.
One of the things which often confuses Christians is that passages like I Corinthians 7 contain both commands and preferences. For example, Paul preferred that Christians remained unmarried during the current distress. "But I say to the unmarried and to the widows: It is good for them if they remain even as I am; but if they cannot exercise self-control, let them marry. For it is better to marry than to burn with passion" (I Corinthians 7:8-9). Notice the use of the words "good" and "better." Paul is not making a hard rule not to marry, but saying that being unmarried at this time is the better position if one can do so.
Marriage to an unbeliever is much the same. It isn't the ideal circumstance. It is much better to marry someone who shares your views of the Lord, but the fact remains that a person can end up married to an unbeliever. It isn't a sin, and that is what Paul argues in I Corinthians 7:12-16, but neither is it a perfect situation.
The same point can be argued from I Peter 3:1, "Wives, likewise, be submissive to your own husbands, that even if some do not obey the word, they, without a word, may be won by the conduct of their wives." Once again, how the situation arises is not addressed and it should not be imposed when the Lord was silent about the matter. The plain fact is that it is possible for a Christian to be married to a non-Christian.
Generally, people argue against the marriage to a non-believer by citing II Corinthians 6:14-7:1,
"Do not be unequally yoked together with unbelievers. For what fellowship has righteousness with lawlessness? And what communion has light with darkness? And what accord has Christ with Belial? Or what part has a believer with an unbeliever? And what agreement has the temple of God with idols? For you are the temple of the living God. As God has said: "I will dwell in them And walk among them. I will be their God, And they shall be My people." Therefore "Come out from among them And be separate, says the Lord. Do not touch what is unclean, And I will receive you." "I will be a Father to you, And you shall be My sons and daughters, Says the LORD Almighty." Therefore, having these promises, beloved, let us cleanse ourselves from all filthiness of the flesh and spirit, perfecting holiness in the fear of God."
The point Paul is making is that Christians are to avoid situations where one is bound in service to an unbeliever. But take note of the phrase "unequally yoked." It is for situations where the unbeliever has power over the believer. This doesn't apply to a marriage. Marriage between a man and a woman is one of equality. Men and women have different roles to fulfill within marriage. Men are to be the heads of their household, but women are not subservient to their husbands. They voluntarily follow (submit to) their husbands. The relationship is still one of equality. "Husbands, likewise, dwell with them with understanding, giving honor to the wife, as to the weaker vessel, and as being heirs together of the grace of life, that your prayers may not be hindered" (I Peter 3:7). Just as Christ is equal to the Father (Philippians 2:6), but at the same time submitted to the Father's will (John 5:30).
The reasons for not tying yourself to an unbeliever are still important to consider and I don't advise any Christian to marry a non-Christian, but I also know that many won't listen, so I help them the best I can in dealing with a less than ideal situation.