Searching on "jQuery Menu," I did not see a specific jQuery menu -- there seem to be several available. Which are you using?
One possibility, though, is to use the CSS-friendly Menu Control Adapter. You can have ASP.NET output the menu as a much cleaner HTML list rather than a table, then use CSS and jQuery to get your client functionality. That way, the built-in Membership menu "pruning" will work and you have much more "style-able" and "jQuery-able" HTML in the page.
After looking at the Plugin
Looking at the HTML used for that menu plugin, I would certainly give the CSS-Friendly Menu Control Adapter a try. It generates nested Unordered Lists of the type that the plugin uses. It should work for you. ASP.NET will generate the menu items that match the permissions in the Membership DB, then you should be able to hook up the jQuery Menu plugin. The Menu Control Adapter wraps the list in a div, but the Menu Plugin can handle that (Example 3). If you need an easy way to find mangled ASP.NET control IDs client-side, I have found the :regex selector plugin to be very handy.