I've spent a bit of time loking into this, and the best solution that I've found was to install unoconv on the server, and using PHP to interface with it through system calls.
I would have loved to find a good native PHP solution for this, but unfortunately I couldn't.
Edit
Since originally answering this, I've come across a web service which presents an API for converting documents. I haven't tested it very thoroughly but it does seem to produce decent results at converting Word to HTML: CloudConvert.
