There are only two ways I know of to get the result you are looking for.
Easy was is the set the server to parse html files as php files.
In apache you would do this by editing the fairly obvious line in the /etc/httpd/httpd.conf file.
In IIS you would open the IIS configuration control panel for the website
IIS - right click on the site name in the services mmc - choose properties - click on the tab labeled "Home Directory" - then click the button labeled "configuration."
The control panel that is open at this point is where you tell the system to send files with the html extension to the php dll which parses the files for the php code.