bridging and NAT in a linux is possible?

Hello, all.

Is it possible that I can use Bridging and Nat simultaneously at a linux 
box which contains 3 or 4 ethernet interface?
I would like to use like this.

for example, eth0 and eth1 is bridging like br0
                   and eth2(Private, 192.168.1.0/24) and eth0(Public, 
58.1.2.3) is NAT.

                       +--------+             +--------------------------+
internet  <----> eth0 | bridge | eth1 <----> | DMZ with real ip          |
                      +--------+             +--------------------------+
                         eth2
                          ^
                          |
                      +--------+
                      | private   |
                      | network |(192.168.1.0/24)
                     +--------+

1. Is it possible?
   eth0 is used bridging and NAT simultaneously?
   If not, 4 ethernet interface is required?

2. If possible, how can I setting?
   eth0 which includes br0 can be public ip rather than 0.0.0.0?

3. If someone in a private network connects to DMZ(from eth2 to eth1)  
   eth2 network is NATed or not?
   again, DMZ can see Private ip(192.168.1.x) or Nated public ip(58.1.2.3)?


Sorry for poor english and 
so thanks in advance.

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