Are you downloading the ZIP files from web (using a web browser, I mean)?
If yes, you can configure the Web Shield provider accordingly - leftclick avast! tray icon to open the on-access scanner console, expand to detailed view, select WebShield and click Configure.
You can set the exceptions on the 3rd page - either in the form of MIME types, or URLs; I guess URL in the form "*.zip" would do.
On the other hand, I don't think there's any reason avast! should interfere with the download process this way...