From my experience as Jimmy mentioned we can integrate modern systems with legacy apps such as mainframe.
I have worked on
Java Application (Front End) that uses JMS to transfer XML files/messages to the Backend for processing. The front end creates an XML file and stores them in the MQ Queue which then invokes a shell script that will pass the message to a COBOL program for further processing and creating reports, Update the database or bulk file processing etc, etc.
Hope this helps.