Interesting. I reckon your current setup (with no reconfiguration) has to work the following way

browser → WebWasher → WebShield → Internet

because WebShield is only filtering traffic on port 80 and this is what WebWasher is using to get the data from the servers.
You could try to configure it like this:

browser → WebShield → WebWasher → Internet

which would require you to set up things manually. Please see my instructions on how to do this here: http://forum.avast.com/index.php?topic=11294.0 (in this case, address_of_your_proxy_server is probably localhost (or 127.0.0.1, which is the same).

Cheers
Vlk