Can a muslim woman marry a non-muslim man?

I am in love with a woman who is a muslim, however I am not a muslim, I am an atheist. Her family does not agree with our marriage, however we really want to get married to each other. She is 23 and I am 29. She is a strong believer in the islam and she doesn't want to do something wrong. I think she should be able to choose who she wants to marry. I will allow her to go to a mosque and pray however much she wants. She can still be religious and a muslim. But we will not get married in a muslim way (?), we will just get married officially at the register office and not in a church or mosque or anything like that. As I said, her parents do not want her to marry me because I am not a muslim. Can we get married without it being a sin for her? Is she as a believing muslim allowed to get married to an atheist?? Thank you for answer!