How can applets from different codebases on the same HTML page communicate with each other?

You can use JavaScript and LiveConnect as a bridge.

Let's say you have applet A and applet B.
You should write 2 JavaScript called sendMessageToA(var s) and sendMessageToB(var s).
Then applet A calls sendMessageToB(). sendMessageToB invoke a method on applet B, delivering the message.

And viceversa.