The Army conducts land combat operations in all types of terrain. The Air Force provides the capability to control and exploit the air and space. In short, the essential purpose of each service is to fight the war in a different medium. They operate under a unified commander because no service acting on its own can provide the expertise and capability to fully exploit warfare in every medium. However, working together they form a mutually supporting, effective fighting force.
Modern warfare is extremely complex.
Operations that are not in a service's primary medium are conducted to support their ability to operate in that primary medium. The Army, for example, flies helicopters not to control and exploit air and space, but to protect its ground forces, to move rapidly over terrain, and to destroy attacking ground forces. Over the years, the services have expanded these supporting activities to include numerous areas which aid them in performing their main functions, but which are really tangential to them. Unfortunately, over time those supporting activities often have come to be viewed as additional primary missions. As with any large bureaucracy, the services have become protective of their investment of time,effort and money into these activities.