You should change the click event from CLICK to MOUSEDOWN.
<html>
<body>
<div id="outerEditor">
<div id="innerEditor" contenteditable="true">
<img src="test.png" />
</div>
</div>
<script src="http://ajax.aspnetcdn.com/ajax/jQuery/jquery-2.1.0.min.js"></script>
<script>
$(document).ready(function(){
$("#outerEditor").mousedown( function(){
alert("click");
});
});
</script>
</body>