I did this on an XP machine for years without any problems and no bridging was necessary. I also did it with a Win2K machine after the XP machine died. I did have Internet Connection Sharing enabled so that the devices on the private network could get to the Internet through the "router" machine, but that wasn't necessary for the "router" machine to be able to access either network.
I suspect the difference may be that the Internet facing side was connected directly to my cable modem, so it was smack dab on the Internet with a routeable IP address and all, and the local network side was on a non-routeable subnet.
Steve, I suspect maybe both of your NICs are on private networks, with a router between your computer and the modem. And each network is possibly on the same subnet, like 192.168.1.x, even though they're on the different physical networks, so Windows doesn't know which way to go to get to the Internet.
What do you mean by "Trying to do this on Win7 the NIC always disables the WiFi"? Do you mean the adapter literally gets turned off, or do you mean it just doesn't pass Internet traffic through it?
Regardless, if they are both on 192.168.1.x, for example, try moving one to a different subnet, such as 192.168.2.x. As long as you use 255.255.255.0 for the subnet mask on each one, then they will be different subnets.