I suppose you could do your if statement then store your message in a variable.
<?php
$message="";
if(isset($_GET['complete']))
$message="<div class='success'>Action was completed successfully</div>";
include(yourpage.php)
Then output the variable on the HTML page.
<html>
<body>
<?php echo $message; ?>
<form method='post' action=''>
...
Another thing you could do is have the HTML page read by php and have "placeholders" that will be replaced by php variables.
Then output that to the user.