Try:
AddType application/x-httpd-php .html .htm
UPDATE 1
It may be PHP version specific. If you're using PHP5 try:
AddType application/x-httpd-php5 .html .htm
UPDATE 2
Try:
RemoveHandler .html .htm
AddType application/x-httpd-php .php .htm .html
Or here's yet another alternative way to do this:
<FilesMatch ".html$">
ForceType application/x-httpd-php
</FilesMatch>
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