I am not having any issues with Zone Alarm Pro (FW/AV) v.5.5.094.000, while also using Avast Home v. 4.6.684. In fact, I am more than pleased with this combo, over my previous set-up... (hungry) Norton 2004/2005 (tried both)
I use 6 of the 7 on-access scanners, only because I don't use Outlook Express.
The only issue I ever had with the Avast, was I tried to dnld Panda Titanium, and Avast mis-took Panda as a threat, (Kuang2-Trojan) even though it wasn't. This could be atttributed as a conflict between apps only.