If I remember correctly Firefox ships with some fonts of its own. For Chromium and possibly other programs, you need to install Chinese fonts. I usually use arphic fonts: fonts-arphic-ukai, fonts-arphic-uming

Firefox's rendering engine will substitute glyphs from other installed fonts (if it can find one with the required glyph) instead of displaying broken glyphs. Chromium will stick to the specified font(s) instead, and will display a "missing glyph" character if the glyph is not found. 

For Chromium and possibly other programs, you need to install Chinese fonts. I usually use arphic fonts: fonts-arphic-ukai, fonts-arphic-uming.