There are numerous way in setting up a DMZ zones. As mentioned, your current design does not caters for one.
Two most common method of setting up a DMZ is the sandwich method and the single gateway method. (Some network which have multiple DMZ have a more complex design.)
Sandwich
Internet---Firewall---DMZ---Firewall---Internal
Single Gateway
DMZ
/
Internet---Firewall
\
Internal
Both design can offer you the same level of security, provided the fw policies are defined properly. However the Sandwich configuration does offer additional security, when the fw is the victim, as the intruder would need more time to penetrate the second fw to access the Internal network. Thus giving administrator more time to respond.
Sandwich configuration also offers better performance as the task for policing the DMZ and the Internal is divided between two fw.
Single gateway design is more cost effective, and usually suitable for companies which provide minimal incoming services and does not provide mission critical services. E.G Only company webserver or mail.
Several questions you need to ask when deciding which design to use.
1. What is the level of security does the company require.
2. How mission critical is the Internet services the company offers.
3. How much are the company willing to pay for security.
Sad to say in IT, the higher the price the better the solutions ... be it isproducts or services.
You might consider adding an addtional interface into the the PIX firewall, if upgradable and go for a single gateway. Else if the only way you can get another interface is to upgrade to a new model, then might as well go for the sandwich.