Which part are you stuck with - using tabs, displaying HTML, compiling for the MS JVM, ... ?
Have you considered letting the browser do the display? You could have the applet in a frame at the top of the page, and on each click on a tab display the corresponding URL in a frame that takes up the bottom part of the page. Even better, can't you just use HTML? It sounds like a menu of links does what you are asking.
If you really want the applet to display HTML, have a look at the JEditorPane class of Swing. It can be used with the MS JVM by way of the JFC/Swing 1.1.1 classes that are downloadable from this page.