Well, one of three ways could work for you.
The linux box hasn't been told that it needs to route traffic from one interface to the other.
1) use a seperate /24 network and route the traffic.
2) use iptables and NAT for your windows box.
3) create a bridge of the two interfaces (eth0 and eth1 act as two ports on a switch)
I'd say option two or three are easiest.
Option 3 will allow your windows PC to communicate with other computers on the network from your router. Personally though I prefer to have my network separate from others in case of viruses/worms/etc so I would go for option 2. You should be able to use iptables with option 1 as well to filter out unwanted traffic.
Like Sibe suggested, we'd like an output of what you have for networking. I don't want to go taking the time to make two or three different configurations for you since you're probably only going to pick one.
Though I have to admit I've not tried doing option 3 before, but from what I've read it looks quite easy. bridgeutils is what we'll be using if you want to look into it.
Oh and there is a secret fourth option. Install virtualbox on your linux box, add the two interfaces into a virtualmachine in bridged mode (so it gets to use them as well as your host linux box.) And install pfsense (or your other favourite firewall distro) and use that.
