You'll need to break up header.html into two files... header.html and subheader.html unless you want to use something like Smarty.
But you could...
include("header.html");
if ($something) {
include("subheader.html");
}
// Or
include("header.html");
if ($something == "show_subheader") {
include("subheader.html");
}
// Or Maybe
include("header.html");
if ($_SERVER['PHP_SELF'] == "mypage.php") {
include("subheader.html");
}