That's not a bad combination. Lots of organizations are doing Java and mainframe integration and many Java folk don't even know the CICS vocabulary. You may find you have exactly the right skill combo for some company. I'm on a J2EE project now, but we have (and need!) a couple COBOL folks yet.
So you probably should grow your vanilla J2SE Java skills and get J2EE
servlet and EJB training or self-training at some point. Then Google for Java CICS integration tools. IBM has a variety of connectors, database vendors, "enterprise integration" vendors and terminal emulation vendors have others. MQ-Series is also pretty cool. IBM even runs EJBs on the mainframe in a Unix partition with APIs to and from CICS, but that sounds just too weird for me.

Any mainframe UDB experience will translate well to AIX-UDB, too.
Big companies like mine think J2EE when they think Java apps. So finally, yes, a track that includes EJBs and Servlets would be good around here at least. Good luck!