I really do not see the point of installing both programs. I think Zone Alarm Pro is the superior product, I doubt that Norton's Internet Security will catch any nasty packets that are not filtered out by Zone Alarm. As for whether it is possible to install both on the same machine, I do not know, but I have a feeling that it could get ugly. On Windows 2000 ZoneAlarm's monitoring component runs as a service that cannot even be shut down unless you decide to remove the entire application. I do not know Norton's firewall, so I cannot comment on that, but I think that Zone Alarm will be the "ruling" firewall. I think you might be facing instability issues if you install both. I sure would not do it nor would I recommend anyone to do it, for the reasons I spoke of.
But then again, it could be fine. It worked for Staver. I wonder what OS he has.
Good luck if you decide to do it anyway. You might want to back up your system.