You can place any machine anywhere you like provided that NAT takes place if that machine needs to communicate onto the internet, or needs to be accessible from the internet.
A standard setup is to have your private, corporate machines on a highly secure internal network running NAT (or PAT - port address translation) and having little or no access to this subnet from anywhere else.
A DMZ can be set up to run public or private (with NAT) IPs, and have limited access to the devices on there, usually devices that need to be publicly accessible from the internet (mail servers, web, etc.).
Since public devices must have a public IP, your machines will still be subject to attack. As always, the best prevention is to keep up with the patches, have an effective firewall policy and pay attention to what is happening on your network.
Hope that helps -