Welcome to FT!
Search is always your friend in a case like this.
There are multiple threads about connecting at MUC.
This one http://www.flyertalk.com/forum/miles...MUC+connection from the LH forum.
Also these ones from here in the Germany forum http://www.flyertalk.com/forum/germa...MUC+connection and http://www.flyertalk.com/forum/germa...MUC+connection and http://www.flyertalk.com/forum/germa...MUC+connection.
Basically, MUC is one of the best airports to connect. You should have more than enough time.
Connecting on two different tickets (PNRs) can be problematic. If your UA flight is late, then AZ is technically under no obligation to accommodate you, and may charge you extra.
Be sure to bring your AZ ticket details when you check-in with UA. United has an interline baggage agreement with Alitalia, so your bags should go through to your final destination of FCO without needing to be picked up in MUC. That said, on the return, AZ may not be so accommodating.