The use of PHP within .shtml files is of acute interest to me, so I've been closely following this thread. (My site currently uses .shtml files across the board without PHP, but I want to be able to include PHP, along with SSI, within my files.) I tried the
>AddType application/x-httpd-php .php .shtml
as noted by others, with the same effect: a request to download a file.
Now that I see that others are running into the same issue I had, I did a search on the web and turned up a number of people saying that servers can't parse for both SSI and PHP together; it's one or the other (e.g., http://www.webmasterworld.com/forum88/1015.htm).
In other words, it appears that what I want to do is not possible, and that I will have to convert all my files from SSI to PHP so I can get at the other PHP functionality I want to use.