Ok, I just got a joystick for my flying in ArmA II and I am running into the same issue as BlackLord. First, rotorwing aircraft and planes are completely different in controls, dont think that if a plane acts one way then a helicopter will do the same. IT WONT! I am talking real life here. BlackLord is correct, if the pilot inputs forward cyclic, the nose will pitch down, the more input the more pitch downwards. If the pilots pulls the cyclic backwards, the nose will pitch up. So yes, push forward on the joystick and the nose should pitch down and pull the joystick back to center and the nose should return to level, not saying you are going to go into a hover, depending on your power input, you will continue whatever forward momentum you had, and most likely even gain altitude.
I am also looking to see if there is a fix for this in the game controls for Helicopters. One modification i have found to be helpful: since most joysticks come with an auto center, something I personnaly hate since i fly helicopters, i took a couple zipties and tied a couple twists in the spring together to lessen the power of spring to center the joystick. it helps, but cutting the spring out completely is the best.