Are you sure the characters are in the font?
Browsers search other fonts to find missing characters - therefor you cant use browsers to test font contents.
You can't trust applications either - here I am using an Arabic font in Notepad to show Chinese characters that I strongly suspect are not in the Arabic font. It seems to me the application (or the underlying Windows libraries) are searching other fonts to provide the missing character.
If you need an independent corroboration, you could try FontForge or another third-party font tool.