What are the roles and purposes of each server?

If the front end is to just handle webmail and active sync, then you should have the backend server handling the mail

SpamFilter can be installed on a server shared with other applications, Exchange included. In your case, the way we understand it, the DMZ server will host OWA, which usually is used only as a GUI to Exchange, it does not actually receive and process emails. In this case it's even easier to install SpamFilter on that OWA server, as you should not have conflicting applications that all try to use the SMTP port. You can siply install SpamFilter to listen for SMTP traffic, and to forward emails to your back end Exchange Server. OWA on the SpamFilter server will server client requests on the HTTP ports, and thus won't interfer with SpamFilter.