How do I interface a C++ application using CORBA with a Java server using RMI.

This is where the RMI-IIOP specification comes into play. Using RMI-IIOP, your RMI object could be exposed as a CORBA object. This means that your C++ CORBA server can talk to the RMI object as another CORBA object. The values passed into and from the RMI methods should be valid RMI-IIOP types.