I would certainly agree with you that the Bible clearly teaches that a Christian should marry only a Christian (1 Corinthians 7:39; 2 Corinthians 6:14-18 – though the 2 Corinthians text is not specifically speaking about marriage).
I would also say that the Bible gives us words of counsel about associations with the ungodly (Psalm 1:1; Proverbs 20:19; 22:24; 24:21). Paul also teaches that Christians should separate themselves from those who profess faith, but who live in open rebellion to God’s word, and to the admonishment of fellow-believers (1 Corinthians 5:11-13). In this text, he tells us that he was not advocating that we avoid all contact with unbelievers.
My own conviction is that one should date only those he or she would be willing to marry (from what they know of that person at the moment). To date a non-believer is to pursue a course of action that cannot culminate in marriage, without clear disobedience. Thus, why proceed down that path. Proverbs tells us that the wise look ahead and see danger, and avoid it, while fools press on. I think that dating unbelievers is unwise, but I cannot quite say with as much dogmatism that it is clear-cut sin, and that one should be disciplined for doing so.
There is also the danger of falling into sexual immorality. In this case, there is sin, whether the relationship ends in marriage or not. It seems to me that there is no complete list of sins for which a person should be disciplined. We do tend to be selective about those sins which prompt us to act in accordance with Matthew 18. In our church, sexual immorality has been the basis for almost every instance of church discipline, but surely there are other sins that should fall into the discipline category. I think that the sins we discipline must be clearly defined sins in the Bible, sins for which there is ample proof of guilt, sins which have been pointed out, but sins that are persistently practiced, without repentance.
I think that most of us tend to discipline only after things have completely fallen apart. One of the words that we find in the New Testament is the term "admonish" (Romans 15:14; 1 Corinthians 4:14; 1 Thessalonians 5:4; 2 Thessalonians 3:15). Admonition is warning. When we see a brother or a sister heading toward danger, we should warn them in advance, and not wait until the disaster strikes. In my opinion, the person you are describing needs admonition at this point in time, not church discipline.
You may wish to look at Hampton Keathley's paper on church discipline.
I hope this will provide some help.