Just installed the Microsoft HTML Filter 2.0 and tested the Edit / Copy as HTML command. I am pleasantly surprised. You can copy either a portion of your document or the whole thing.
It even includes css classes with the same name as the Word Style. We use styles extensively and to see this included is a plus. Now we can add those classes to our themes to make the output even more professional-looking.
On the downside, it includes font information within span tags and bullets are hardcoded as a (too small) character from the Symbol font.
In order to use the data that has been copied to the clipboard, click on the <> button in the editor to get to source mode and paste. Then click <> again to see the results.
An explanation of what the utility does can be found
here.
There is a command line version of this filter utility which is more powerful but less convenient. Instructions on how to use it can be found
here.