Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
It is not permissible for you to accept the gathering of a man with an alien woman (girl-friend) in your house, because there are some disobediences (sins) that result from this, like the forbidden looking, forbidden speech and the establishment of a relationship between a man and an alien woman, let alone your arranging this meeting in your house. All of that is considered as an acceptance of the sin for the sinners, being pleased with it (with the sin) and making it easy for them.
Allah forbade the Mu’minun (believers) to sit with the sinners (while committing the sin).
Allah Says (interpretation of meaning): {…then sit not with them, until they engage in a talk other than that; (but if you stayed with them) certainly in that case you would be like them….}[4:140]. And Allah Says (interpretation of meaning): {…Help you one another in AlBirr and AtTaqwa (virtue, righteousness and piety); but do not help one another in sin and transgression…..}[5:2].
Therefore, you have to clarify this with your friend in a wise manner, and inform him that you wish to keep relationships with him, but your religion forbids that your house be a shelter or a meeting place for what Allah is not pleased with.
If he marries that woman Islamicly, then there is no harm for you to visit him.
The important ways of Da’wah are wisdom, good admonition, quiet debate and the use of every opportunity, especially having a smiling face, being kind and good to people, without forgetting giving gifts, books, beneficial tapes, CD’s and so on.
However, first and foremost you should be keen on calling the neglecting Muslims to Islam, more than the non-Muslims.