Airport Extreme Name Resolution
Apple's DNS resolution expects a tiered solution, so you will want to simply point the router and clients to the internal DNS.

That DNS will answer all queries for it's internal responses and refer/forward requests outside it's authority to the outside DNS of your choosing.

In short, you will either need to change your internal DNS or set up a third DNS to know what requests to handle internally and which externally as the AirPort wasn't designed to do that choosing for you.

Here's how you would set up OS X server DNS to do forwarding - it's a simple pane where you place the external addresses.