Crystal ball says you're on shared hosting. Before you tear out any more hair, take a look at their own docs, including the wiki if there is one. They may give the formula for permitting php within html. On mine there's no separate mention of php at all; the bit that enables include files (which may happen to be php) is
AddType text/html .html
AddOutputFilter INCLUDES .html
The first line seems like a tautology -- "html should be read as html" -- but you don't hear me arguing.