Can i "a catholic" and my Bf who is muslim has a big possibility to engage in marriage without converting?

My bf is muslim and i am a catholic,we had many times talking about our religion and we have not yet decided who's religion must be followed..He already met my family and so do i..we already talked about marriage..but, my parents don't want me to become muslim,they always reminds me if i will marry my Bf he must be the one who will be converted.My Bf on the other side don't want to become christian,but as he always said he loves me and he want to marry me..I asked him " if i will not convert into muslim would you still marry me?"He just sigh and said "I'm not sure" "I don't know" etc.What should i do?Does he loves me or not?..Will i continue my relationship to him or get over?Do muslim have no right to become christian?...Pls help...thnx..