can muslim man and christian woman get married? or christian woman should become muslim?
A lot of that depends on your husband to be. Have you discussed this with him.
The muslim faith is very much about keeping marriage unified, and that includes religious beliefs. A muslim man is expected to marry a virtuous muslim woman.
The Quran states :
This day are (all) good things made lawful for you. The food of those who have received the Scripture is lawful for you, and your food is lawful for them. And so are the virtuous women of the believers and the virtuous women of those who have received the Scripture before you (lawful for you) when you give them their marriage portions and live with them in honor, not in fornication, nor taking them as secret concubines. Whoso denies the faith, his work is vain and he will be among the losers in the Hereafter. [Qur'an: Al-Ma'idah (5:5)].
Muslim and Chirstian faiths are not as different as people would like to believe. There are factions of muslims that have doctrines that traditional muslim beliefs do not follow.
Ultimately, the answer is going to depend on how closely either of you follow your beliefs. Since they are not the same, neither of you will understand the others, and therefore that will be an aspect of your life that you can not share.
If that does not bother you, and it does not bother him, then I wouldn't worry about it. If it does, you will need to come to a comprimise BEFORE you get into marriage.