Is it possible to use multiple programming languages on one website

Yes, it is possible, but you definitely should NOT do it.

Communication between pages running different technologies will not be elegant, if for no other reason than the fact that you won't get a shared session pool. Session bridges are possible, but they are a pain to do.

I would say you are making a mistake if you can't just pick a single language for your core web layer.

Yes. It's possible. Where you will find yourself in trouble is when you want to share server-side information among them (I.E. sessions).

Other than that, you can use (but I would advise against it) all languages you want on a website.