I've used the markitup library for the Rich text editor for my project.
However I need to make it in live editing mode which I mean, when I type a text then make a selection Bold, Italic or Strike-out it would render directly in the textarea without have to do a preview.
Something like with MS Word of Open Office Writer.
Checking with Firebug, markitup injects a iframe to do "preview" the text.
From the markItUp home page:
markItUp! is not a WYSIWYG editor, and it never will be.
What you are describing is a WYSIWYG editor. If you want to use one, I recommend something like: http://ckeditor.com/