Hi,
Seems you are using software 8.2 or something below.
Dont think you are able to configure the above Static NAT and make it work.
Notice that if you wanted to only forward a certain port with Static PAT then the configuration would look like this
static (dmz1,outside) tcp 4.4.4.4 80 192.168.1.2 80 netmask 255.255.255.255
static (dmz1,outside) tcp 4.4.4.4 443 192.168.1.2 443 netmask 255.255.255.255
Though even in the case of the above Port Forward / Static PAT configuration I dont think the ASA will accept the configuration.
EDIT: Meaning that you cant do the above configuration for both of the Internal DMZ hosts.
On newer softwares you can forward the same ports to different hosts BUT I still think it will not work in a situation where you would want anyone to be able to connect to both of the hosts. You would have to modify the NAT rules to apply only to certain source IP addresses on the Internet.
- Jouni