Out of curiosity I tried running this XHTML document in IE6, and both the borders displayed ok, so I don't know what the problem is!
Code:
<?xml version = "1.0"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns = "http://www.w3.org/1999/xhtml">
<head>
<title>Template</title>
</head>
<body>
The text
</body>
</html>