see attachement...IP addresses have been changed to protect the innocent.

I'm confused on the designations of Public and Private when configuring
the interfaces. I have NW6.5sp1 with BM3.8 and just default packet
filters. When I ping from my BM server, I get the IP
address but no return ping. When I disable packet forwarding filters, I
can ping just fine. I understand that by default, all
traffic is blocked to and from the PUBLIC interface.

However, as found in the diagram, I have a DMZ (Private) interface
attached to the same switch (logically) as my PUBLIC (Public) interface.
Shouldn't I still be able to ping regardless of whether
the filters are turned on or off? I expected to get a response through
the DMZ (Private) interface simply because there are no filters set for
this interface (by the default filters) and it is attached to the same
network as the PUBLIC (Public) interface.

Disclaimer...This configuration is not the final production
configuration but an interim configuration for testing and moving to
another configuration (see future DMZ network in diagram).