You can't distinguish closing the browser from navigating to another page. In both cases the current page is unloaded.
update: maybe you can handle some cases with some jquery, i.e. whenever a link is clicked, set some flag to be able to distinguish it from closing the window or entering a new URL:
<body onunload="checkForClose()">
...
<script>
var _isNavigation = false;
$(document).ready(function () {
// whenever a link is clicked set _isNavigation to true
$('a').click(function () {
_isNavigation = true;
});
});
function checkForClose() {
// show an alert if _isNavigation is not set
if (!_isNavigation) alert("closing the browser (maybe)");
}
</script>