For some reason the BES setup didn't put a message w/globe icon on my main screen. 

However, when i went to the main screen and clicked "show all", there was the separate icon for BES. 

So I kept the BES icon and also kept the icon for my Verizon email, but hid the icon for the inbox that combines all messages together.   So I got what I wanted - segregating two inboxes on the main screen.

Thanks to those who responded. 

PS.  I can't believe the typos I left in my original Subject line 🙂