<html lang="ja">
Japanese text ...
<span lang="zh">
Chinese quote
</span>
...
</html>
is much easier than mixing encodings. With the above entirely in Unicode, it will be handled reliably by anything that can handle Unicode, and is still reasonably readable even if the Chinese text is shown in a Japanese font. Reading just the fourth line without the third will still show something 'OK'.
Mixing Shift_JIS and Big5 sounds like a recipe for corruption, but something similar was done in an old Russian and Japanese encoding: https://en.wikipedia.org/wiki/Shift_Out_and_Shift_In_charact...
RFC 2482 was a Unicode adaptation of this, but it was deprecated 12 years ago: https://www.rfc-editor.org/rfc/rfc6082.html