Why should they have to be a �believer�?
If they accept you for who and what you are then they may also respect your beliefs and your desire to stay with a church which will not accept cohabiting outside of marriage. If they don�t then you have a decision to make although judging by your post, it would probably be already made for you.
If you are referring to a person outside of your church, then you either have the freedom of choice to forgo the relationship, hope that they respect your beliefs, or let them decide whether they want to share your beliefs and join the church or not, and then accept and respect their freedom of choice and decisions.
If it is someone inside of your church, then I presume you would both feel the same way anyway.