Building an infrastructure for developing web-applications using multiple programming languages(Python Java C#)
It is certainly possible. For example I have developed web applications using a mix of:

Java (for back end interfaces, APIs and performance-sensitive code)
Clojure (for the main web app on the server side)
JavaScript (for client side code in the browser)

Overall, this has worked pretty well in that you can use each of the languages for their specific strengths. Though you should be warned that it does require you to be pretty multi-skilled in all the languages to be effective, and it does require a lot more configuration of your environment to get everything working smoothly
Tricks I have found useful:

Be very clear about why you are using each language. For example, JavaScript might be limited strictly to client side code in the browser.
It helps enormously if languages run in the same platform. For example, Clojure and Java both run in the JVM which makes interoperability much easier as you don't need any extra code for interfacing between the two.
Use an IDE that supports all of the languages you intend to use (in my case Eclipse)
Use a good build system with multi-language support. You want to be able to do a "one click build" that includes all the languages. IMHO Maven is the best tool for this (especially if you use something like the Eclipse plugin for integration with the IDE)
I've searched for this on different places but I haven't found an exhaustive answer. Suppose we have separate modules written on different languages each of them realizes certain part of logic. We have not permission for recompile them to certain one language (for example using JPython).
I`m a real novice at this part of programming so it is hardly to find words describing this problem. It seems I try to find something like Maven but for multiple languages and for addition modules may be precompiled.
Is this theoretically possible?