If marriage were only "a piece of paper," then your position might make sense. We could treat marriage casually, and approach it with a "take it or leave it" attitude. Unfortunately, that's the way many people (including the two of you) see it today.
But have you ever asked yourselves what marriage is in God's eyes? To Him, marriage isn't just a nice social custom or a useful legal arrangement. Instead, it is a divine gift–something He ordained for the human race right from the beginning. God gave marriage to us.
Why did God do this? He did it because He loves us and He wants us to be happy and secure. That's why marriage should not be just a pledge that a husband and wife make to each other, but a solemn vow they make to God. The Bible says, "For this reason a man will leave his father and mother and be united to his wife, and they will become one flesh" (Genesis 2:24).
One thing is missing in your relationship: commitment. Yes, you may well love each other–but without marriage, you are not truly and irrevocably committed to each other. But something else is missing in your lives–and that "something" is God. Don't try to live life without Him any longer, but by faith turn to Christ and make Him the foundation of your lives–and your marriage.