If you're running active directory...you NEED TO have your domain controller(s) be the only DNS servers for themselves..and for all client workstations. It is better to run DHCP from the server also...as it allows better registration and updates within active directory, basically keeps active directory running tighter. Microsofts domain..active directory...is built on the foundation of DNS. Without having DNS run properly for your network..,.active directory will be broken. Things may "appear" to work OK on the surface for basic things..you might have browsing network shares working..but it's only appearing to work on the surface. Try to do more advanced things within AD...and you'll find they don't work. Or you may find workstations lose their computer account every now and then.
If your server is, for example, 192.168.10.11, it should run DHCP..and it should have out 192.168.10.11 as the one and only DNS for all workstation. Client workstations should only have 192.168.10.11 for their primary DNS...nothing else. Secondary DNS would be a second domain controller if there was one. ISPs DNS or the routers IP has no business being anywhere in TCP/IP settings DNS settings anywhere on the network.
Server looks at itself for DNS.
You set the DNS forwarders in DNSMGMT.MSC...I like to use the safe DNS services like OpenDNS...to add another layer in malware protection for the network.
Some people say.."but what if my server goes down...I need workstations to still browse the internet! So I put a second DNS in there like my ISP, or Google". Well..if your experience is that servers go down all that much..perhaps consider a career change. Servers should be built on proper server grade hardware so they don't go down. And if you're building servers...you should have the mental capacity to come up with a plan..."Gee..server is down, will be down for a few hours or until tomorrow...let me take 30 or 45 seconds..I can log into the router and enable DHCP there...to fill in for a few hours....give the people the day to surf facebook or whatever..and then when the server is fixed..simply disable DHCP on the router again".