You can't buy and use the Blackhawk in the campaign, but you can see NPCs use them throughout the campaign. However, in multiplayer, Blackhawks are obtainable in every role, with a higher price if you are not an Air role.
The Blackhawk was a revolutionary design during the 1970 and 1980s. The US military had been using UH-1 Hueys in Vietnam and they soon realized a newer and more sturdy helicopter was needed, thus the Blackhawk was born. Ever since its entrance into the U.S. Army, it has been the standard transport helicopter in the Army. The U.S. Marine Corps do not use the Blackhawk, but upgraded versions of the UH-1 Huey.