Iptables INPUT, OUTPUT and FORWARD chains
Solution 1:
I believe you are asking the wrong question. eth1 interface is not part of eth0_input, and eth0_output is not part of eth0_forward - although they may be related in your configuration
- eth0 and eth1 are interfaces.
- eth0_input, eth0_output and eth0_forward are constructs created by your configuration rules, and while descriptive are entirely arbitrary.
Rules are separate to interfaces, although they interact with them.
In general -
Packets destined to the local machine are handled by the INPUT chain. Relatedly, Packets originating from the local machine (ignoring NAT) are handled with the OUTPUT chain.
Packets from other machines behind the router go through the FORWARD chain.
You will most likely find that eth0_forward chain has been used to control what servers & ports are exposed to the Internet, ie traffic originating from eth0 will be traffic from the world, and should only be allowed if - It corresponds to an outbound stream (ie caught by an earlier ESTABLISHED,RELATED rule) or is to a known port on a known system - in which case it should be allowed or rejected before it reaches eth1. THE RULE AS WRITTEN DEALS WITH TRAFFIC FROM THE WORLD BEFORE IT GETS TO THE LAN SIDE OF THE FIREWALL.