You're correct: you don't need to set up NAT or use iptables (although that's certainly a common scenario).
All you have to do is:
1. Configure one NIC for one network, and the other NIC for the other network.
2. Enable IP forwarding.
If it doesn't work, please post back details about the specific problems you're encountering.
And if you haven't already done so, a useful Google search is "linux dual-homed ip forwarding"
Here's a good link:
'Hope that helps!
Just to clarify:
I need this system to route traffic between the 108 and 109 segments
<= No problemo! Easy. See above.
I can set up the router system as the default gateway for all other systems
<= You definitely need iptables if you want to exchange packets between your LAN(s) and the Internet
A good Google search for this latter scenario is "linux internet connection sharing"