You can convert a DOCX to EPUB with calibre -- whoever told you to use filtered HTML should be punished!

I am not even going to try to guess what filtered HTML will result in.
Just convert DOCX ==> EPUB.
Or better yet, calibre's Edit Book feature can open DOCX and save as EPUB, and if you want to tweak the HTML it is a better route -- conversion is intended as the last step before reading a book, and makes certain assumptions (flattened CSS) that don't help you edit the ebook.
EDIT: When you say "marked all the chapter headings <h1> Heading </h1>" I assume you mean "marked all the chapter headings with the header 1 style".