DMZ DNS configuration best practice

Hello all,

I just inherited a network where they are using public IPs for everything in the DMZ. The firewall is configured in “drop in” mode and all DMZ servers have public IP’s.

My question is in regards to configuring DMZ DNS servers. Our exchange server is in the DMZ and authenicates to internal DC’s. This servers primary dns points to internal dns server and it’s secondary points to a dmz dns server. Can you tell me what the configuraton would look like for this setup.

The DMZ dns servers are configured with our internal dns zone records for our 2 interal DC’s. Isn’t it a bad thing to host internal dns records on public facing servers?

Please help!