It looks like perhaps you saved the file as a UTF-8 file (or an ISO-8859-1 file, perhaps), and the encoding doesn't match the encoding specified in your header (i.e., Big5).
If you're going to mix CJK and non-CJK content, your best best will be to use UTF-8 consistently throughout the whole site.
It might also, of course, be the case that Dreamweaver sucks at CJK support, I've never tried. By handcoding the pages, you can make sure that it works.
When you say it's no problem when you “preview in Safari or Firefox”, do you mean via Dreamweaver's built-in preview function, or by opening the file on your hard drive in Safari/Firefox? If the latter, then the problem could also be that you've uploaded the file as a binary where it shouldn't be (or vice versa) in FTP.