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In order to parse html files as php, add the following line to your .htaccess file:
AddHandler x-httpd-php .html

This is different than:
AddType application/x-httpd-php .html .htm
(Which will not work with SuPHP)

This can also be done with CPanel using the Apache Handlers link. Add the following entry:
extension: .html
handler: x-httpd-php

Thanks to Ed at LP Support for help with this!

REFERENCES
http://www.lunarforums.com/php_and_mysql_support/suphp_htaccess_to_parse_html_as_php-t15889.0.html