The USS Essex class, which is a LHD, typically can handle:
AV-8B Harrier II
CH-53 Super Stallion
CH-46 Sea Knight
UH-1N Huey
AH-1W Super Cobra
In the future it will presumably also handle:
MV-22B Osprey
F-35B Lightning II
UH-1Y Huey
AH-1Z Super Cobra
No, it would not handle the Marine Corps' F18C/Ds. The USMC chose not to upgrade to the Super Hornet (F/A-18E/Fs)as the Navy did in favor of waiting for the JSF. The Navy on the other hand took the upgrade to replace it's aging Tomcat fleet. The F18 has flown off of the Essex
IN PR for balance purposes, but it is not realistic.
Marine Fighter Squadrons are often attached to Carriers however and operate just as a US Navy Fighter Squadron would. So yes, they do operate off of Super Carriers, which can essentially hold just about every helicopter known to mankind as well as many jets, as long as they are properly fitted. Hell, even a C130 landed on a carrier
