There are no user set options for the Network Shield other than not to use it and that would be very bad as it provides a valuable function. Not only in blocking exploit attacks on certain ports but more importantly blocking known malicious sites.
I don't know why your firewall isn't blocking this as the standard windows 7 firewall should bloc these attempts, so why avast is having to act as a fall back is strange.
I don't know if this is just a timing thing in that avast and in particular the network shield is starting before the windows firewall. You could try thin in the avast Settings, Troubleshooting, enable this option 'Load avast! services only after loading other system services' (last option, see image) and see if that helps.