Can't really help you with a direct answer, I can just give a warning. There is a book on java/net interoperability, but before you buy, read the revieuws first. It describes .net and it describes Java, but not a real interoperability between the two.
Now back to your question. There are a couple of approaches, currently the most common one is webservices which can be written and used by java and .net.
On the other hand, it may be enough for your application to export xml from one application and import it in the other applciation. That just depends on the type.
swimming certificate (A & B), shoelaces diploma, and some useless java ones.