Wulf, WebShield intercepts only communication directed to TCP port 80. If this is web browser it must of course connect to this port, unless it uses some kind of a proxy.
Web Shield intercepts only connection from certain limited set of applications. Internet Explorer and Firefox among them. If you want to extend this set to include your browser, you must edit avast4.ini.
(in c:\program files\alwil software\avast4\data folder).
Find the section [WebScanner] and add or edit the line OptinProcess= to include the name of the surfit browser. Multiple names must be separated by comma.
Eg.
[WebScanner]
OptinProcess=surfit.exe, something_different.exe
Restart webshield and try it.
If you'll experience any problems with the connectivity, please feel free to inform us, or send me an e-mail. We have not tested this browser and that is why it is not scanned by default, but there is no reason why it should not work - unless it uses some non standard communication patterns.