Same subnet for 2 NIC in a system

I am presently configuring a firewall with 3 nics. One connect to the internet, one to DMZ and one to private network. Eventually, the nic for both DMZ and internet had to be of the same subnet. Hence, I configured the network as the picture below.
                     | Firewall  |/
                           |             |
                           |          Server
                        private network
The problem is that the nic for the internet and nic for DMZ has a conflict. As the server can ping but not the other way round. However once the nic to internet is disable they can ping each other. How should I go around this?
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You can't do that.

Either you need to subnet into three subnets, or you need to use different C-nets.

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Linux Networking

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