I am looking for a (simple) text editor that can handle text in different encodings in the same document.
I need to develop some sites with mixed Japanese and Englis
Try BabelPad. Editing-wise, it's simple. Unicode-support-wise, it's awesome!
It sounds like maybe the problem with Jedit is the font - are you using a font that can display all the characters correctly?
To be more precise, Arial Unicode MS is a reasonable choice for a Unicode font that can display a wide range of characters across the range of languages. There are certain issues with it that can make it less than optimal for some languages used in isolation - this is why there are also language specific Unicode fonts included with Windows.
On the Mac: SubEthaEdit has excellent support for character encodings.
Emacs correctly handles UTF-8 for me. (And of course, it can edit HTML and PHP files).
TextPad is a good utility too. It's a trialware, but does the job fine. See how to set char-encoding-setting-in-textpad.