The subset of html tags supported is quite poor and has not changed in forever:
<a>, <b>, <br>, <font>, <img>, <i>, <li>, <p>, <textformat>, <u>
This means is that regardless of conversion quality, html cannot be rendered as fully intended; you could also be giving up a significant portion of css styling if you replace unsupported tags with more basic ones.
That being said, http://simplehtmldom.sourceforge.net/ (PHP) would work with some tweaks and it's competent enough to cope with invalid markup as well (seeing how you're after processing content from various sources, I'd say this feature alone would save a lot of pain in the long run) - than replace
<h1>,...,<h6> => <b>
<strong> => <b>
<em> => <i>
and plaintext the rest of it into paragraphs you'd be surprised at how readable it would still be. You could be a bit fancy too like so:
<h1> => <b class="header1">
and add some css as appropriate (although flash css support is pretty limited too)
I've been saving this one for desert - you'll either love it or hate it but it would do the trick. Assuming your app is deployed in-browser (if not and I misread you, save me the embarrassment and stop reading right here) you could use an iframe to display your html, seriously.
JS<->AS communication is fairly straightforward and you could have it positioned over a predetermined area of your app, giving the illusion that it's part of it; just remember to set windowmode on the flash object/embed correctly so it does not render on top of other page elements, then increase the iframe z-index.
I would not be surprised if this is seen as an "ugly" approach, but it's beautiful on the inside - you'll end up with verbatim html and real css support. As for user interactions, you could even intercept link clicks etc. in the iframe and request an action from the movieclip.
