Having separate domains for your DMZs is a good idea. However, you suggest one domain for the two DMZs. If there is sufficient reason to have two separate DMZs, there is likely reason enough to have separate domains as well. Without knowing more about your network setup, it is difficult to know for sure. The different domains in and of themselves probably don't add that much value in the way of security (although they could if the appropriate trust relationships/restrictions are put in place.) However, making it easier to determine who has administrative authority over specific servers is a good thing.
For more info on this topic, check out these SearchSecurity.com resources:
This was first published in July 2003