What @andrew-jackman says is correct, but i still did a fiddle with jQuery for the kicks.
I included a hidden field to manage the data and make used jQuery's toggle to replicate the checkbox functionality
<form action="test.php" method="post">
<div id="test1" value="testvalue" checked="checked">
<input type="hidden" name="test" id="hiddenfield" />
</div>
<input type="submit" />
javascript
$('div#test1').toggle(function(){
$('input#hiddenfield').val('checked');
alert($('input#hiddenfield').val());
},function(){
$('input#hiddenfield').val('');
alert($('input#hiddenfield').val())
})
http://jsfiddle.net/kumiau/nPEYw/1/