You can use DOMNodeInserted and DOMNodeRemoved to check if elements are added or removed. Unfortunately, IE doesn't support this.

$('#myDiv').bind('DOMNodeInserted DOMNodeRemoved', function(event) {
    if (event.type == 'DOMNodeInserted') {
        alert('Content added! Current content:' + '\n\n' + this.innerHTML);
    } else {
        alert('Content removed! Current content:' + '\n\n' + this.innerHTML);
    }
});

Update

You could save the initial contents and future changes with .data(). Here's an example.

var div_eTypes = [],
    div_changes = [];
$(function() {
    $('#myDiv').each(function() {
        this['data-initialContents'] = this.innerHTML;
    }).bind('DOMNodeInserted DOMNodeRemoved', function(event) {
        div_eTypes.concat(e.type.match(/insert|remove/));
        div_changes.concat(this.innerHTML);
    });
});

Example output:

> $('#myDiv').data('initialContents');
"<h1>Hello, world!</h1><p>This is an example.</p>"
> div_eTypes;
["insert", "insert", "remove"]
> div_changes;
["<iframe src='http://example.com'></iframe>", "<h4>IANA — Example domains</h4><iframe src='http://example.com'></iframe>", "<h4>IANA – Example domains</h4>"]

Update 2

You may want to include DOMSubtreeModified as well, because I've found out that DOMNodeInserted and DOMNodeRemoved don't trigger if an element's innerHTML is replaced directly. It still doesn't work in IE, but at least it works fine in other browsers.

try something like this...

    $('#divId').bind('DOMNodeInserted', function(event) {
             alert('inserted ' + event.target.nodeName + // new node
           ' in ' + event.relatedNode.nodeName); // parent
       });

IE doesn't support this propert but i think the nearest to this is the propertychange event, which fires in response to a change in an attribute or CSS property of an element, but it doesn't fire in response to innerHTML changing, which would have been close to what you wanted.

one more feasible solution is to override manipulation function of jquery...

Have a look on this discussion..Preferred way of modifying elements that have yet to be created (besides events)

There is no such an event (onChange) in javascript nor jQuery, you would have to create a custom event.

One solution could be using lowpro to attach a behavior in this element you want to be controlled, this behavior would serialize the element and then build a poll that checks every x miliseconds to see if the element has changed, if changed then trigger your custom event on that element.

You have some examples on how to use lowpro with jQuery here: http://www.learningjquery.com/2008/05/using-low-pro-for-jquery

Good luck!