Iframes can be problematic, as search engines don't often index framed content correctly, and most likely a user following a SERP link to the forum would be taken to the iframe content page. In addition, there are browser differences that could make that approach problematic.

My suggestion would be to use a php command to import a header and footer based on some get variable. Something along the lines of:
if ($_GET['site'] == 'site1') {
require("site1header.php");
}

That way, if your forum is at www.myforum.com/page.php, if the visitor comes to www.myforum.com/page.php?site=site1 they would see the header. Otherwise, no header would display.