For Markdown -> HTML, there is Showdown (this link points to a demo page, which, itself, links to some .zip you can download)
StackOverflow itself uses Markdown language for questions and answers ; did you try to take a look at how it works ?
(I don't know the license, though ; maybe you can just re-use its code)
Well, it seems it is using WMD editor
The question Is there any good Markdown Javascript library or control? and its answers might help, too :-)
A full editor is, of course, not exactly what you asked for ; but they must use some kind of function to transform the Markdown code to HTML ; and, depending on the license of these editors, you might be able to re-use that function...
Actually, if you take a close look at Showdown, in its code source (file showdown.js), you'll find this portion of comment :
//
// Showdown usage:
//
// var text = "Markdown *rocks*.";
//
// var converter = new Showdown.converter();
// var html = converter.makeHtml(text);
//
// alert(html);
//
// Note: move the sample code to the bottom of this
// file before uncommenting it.
//
It's not jQuery syntax, but should be quite easy to integrate in your application ;-)
About Textile, it seems to be a bit harder to find anything useful :-(
In the other side, HTML -> Markdown, I guess things might be a bit harder...
What I would do is store both Markdown and HTML in my application data store (database ? ), and use one for editing, and the other for rendering... Would take more space, but it seems less risky than "decrypting" HTML...