Your checked luggage will go through without problems. Since Croatia is not yet a part of the EU (http://en.wikipedia.org/wiki/Accessi...European_Union), your bag tags will not have green strip on them. So, when you arrive in Rome the customs inspectors could decide to inspect them (in practice they inspect maybe 1% of all luggage).

You will have to clear passport control into the Schengen area in MUC.