Embed HTML5 files/subfolders in post?

This plugin should do exactly what you’re looking for: http://wordpress.org/plugins/shortcurl/ it will allow you to embed a shortcode in your post that should go grab external content and place it exactly how you’d like it to.

Since it’s not an iFrame, you should also be able to style the content appropriately without much issue (if necessary).

UPDATE: Since the whole page may not render properly inside the post context, you might try the following (or something similar) for the shortcurl short code:

[remote_get url="/path/to/index.html" start="<body>" end="</body>" replace="<body>" with="" replace2="</body>" with=""]