I'm not sure what you want to do exactly but if you want to get raw source code from jQuery you can use the following:
var html = $('element').html();
And with pure javascript from an id
var html = document.getElementById('id').innerHTML;
or from classname
var html = document.getElementsByClassName('class').innerHTML;
And to get the content of your example (which is an editor called tinymce) you can use the command tinymce.activeEditor.getContent();
or tinyMCE.get('myTextarea').getContent()
EDIT:
If you want to listen for changes with jQuery and display to html dynamically you'd want to do something like this:
$('yourTextArea').keyup(function() {
var html = $(this).val();
$('yourElementToDisplayTheHTML').html(html);
});