It depends on what Exchange version you're using. If you have Exchange 2007 or 2010, there is a role custom made for living in a DMZ: the Edge Server. Put that server in your DMZ and configure correct ports between that server and your private-network Exchange Hub-Transport servers. If you have Exchange 2000/2003, there is no good solution as far as InfoSec is concerned, you're pretty much stuck opening up SMTP (and TCP/443 if you use OWA) to a domained machine.
Again, depends on your Exchange version. If you're at 2007/2010, the Edge server is designed to operate without any live connection to an actual domain-controller so there is absolutely no need to put a DC in the DMZ. If you're with 2000/2003 the server that's receiving Internet mail will have to be domain-connected somehow, which can be to a DC in DMZ (but with no DMZ/Internet firewall ports open) or to DCs on the private network by way of DMZ/Private firewall policy allowing the traffic.
Keep in mind that "DMZ" does not equate to "all ports open", you can open just the ports you need for both your DMZ/Internet and Private/DMZ firewalls. You can keep an Exchange 2000/2003 server in the DMZ and poke holes in your private/DMZ firewall to allow it to communicate to the DCs in the private network. Yes, it's a stepping stone to having your DC's hacked, but if that really concerns you upgrade to Exchange 2010 where Microsoft has engineered a much better solution to the problem.