You are in a difficult spot, because you are such a new Christian. Something that might be clear cut to a more mature Christian might be very difficult for you. (I suggest you ask for God's help that his will be done.) My thoughts below might be unpleasant news to you, but I only say them because I am thinking about your greatest long-term happiness. Disclaimer: I haven't dated much and have never been married.
Fundamentally God loves you and sacrificed his son so you could be in a positive, thriving relationship with him. The farther down the path to Jesus you look, the more awesome it is for you. Life is difficult even when you are surrounded by supportive Christians (and not an unbelieving boyfriend/husband). I think it would be wise to try to understand what your boyfriend is like when you are under a lot of pressure to do one thing and your boyfriend is under a lot of pressure to do something else.
God is pretty serious about his followers not getting too involved with unbelievers. See 1 Corinthians 7, 2 Corinthians 6, and Ephesians 5. There's also a lot of other passages about the connection between believers and unbelievers. (Your favorite search engine would yield plenty of reading material.)
You may not yet be thinking about marriage, however, if you let your relationship get to that point, it may be too difficult to turn away, even if you think that is what God wants. (I know someone who waited too long, and her thinking changed to justify what she wanted.) A successful marriage is about sacrificial love. Is your boyfriend ready to lay down his life for you? (Ephesians 5:25) If he says he is, why is he unwilling to become a follower of Jesus? Put another way, does he love you more than himself? It is fundamental to genuine love that a person be willing to give up what he or she wants for sake of the other. That is part of what Jesus meant when he said, If you love me, you will obey what I command. (John 14:15, 1984 NIV) (Giving up you want to do what Jesus wants is a form of love.)
The hard part of all of this is that you will eventually need to choose between God and your boyfriend. There really is no such thing as completely "letting you be Christian," because successfully growing relationship (marriage) is a melding of two people. If God clearly told you to move to a different place, but your boyfriend didn't want to leave his job, what would you do? He won't be able to trust God that He will provide another job. Depending on your calling, you may need to make a lot of pro-Jesus decisions.
What if your relationship doesn't work out—a fancy way of saying, what if being with each other comes to cause increasing pain for each of you. From God's point of view, divorce is not an option. (I'm not talking about an abuse situation.) With two people devoted to obedience to God, each will have God's help to work it out, and if each is willing to lay down their lives for the other, it will almost certainly work out. Your boyfriend may only have the advice of unbelievers to help him (a scary thing from my perspective).
Depending on your personality, you might consider is keeping your eye out for a Christian that you are attracted to. Sometimes one of the reasons it is hard to stop dating someone is because the person doesn't want to be alone.
I can assure you that in the long run, you won't regret choosing Jesus over everything else.
And without faith it is impossible to please God, because anyone who comes to him must believe that he exists and that he rewards those who earnestly seek him. (bold mine, Hebrews 11:6, 1984 NIV)