Yamba Yoon,
Having a Jewish mother makes him Jewish. Full stop. (It gets a bit more complicated if it were his only father who was Jewish.) It sounds like your parents are more concerned about the "appearance" of him being a non-Jew, rather than the halakhic issues (as there are none; with a Jewish mother he is considered as fully Jewish as someone with two Jewish parents). Perhaps you can talk with them about their concerns? Ask them why they think he's not "Jewish enough," and find out if it's their own concern or their perceived concern of the community.
Good luck!