How to setup DMZ with Airport behind a router (double NAT issue)?
Out of the box, the Airport (and Apple's Time Capsule) insist that there not be two NAT/DHCP devices chained in a row. You're trying to do this, one being your broadband router, and the other your Airport. In this situation, the Airport will insist on being in bridging mode and letting the broadband router be the DHCP server. 

The Airport detects this situation by looking at the IP address it gets. If it is one in a number of known ranges like 192.168.x.x, 172.x.x.x, or 10.x.x.x, it will balk. 

So the way you get around this is by having your broadband router give out addresses in a range that's safe but not knows as a "private" address range. I found an article [1] recommending a block of addresses designated for "testing" purposes in the Amateur Packet Radio network (AMPRNet). The range is 44.128.x.x.  I set up my broadband router to use that range, and my TimeCapsule is happy to provide NAT as well. Problem solved.

[1] http://www.wa4dsy.com/robot/ooma-airport-hack