The 82nd Airborne is and the 101st are divisions and have a one or two star general running the show. Battalions that are in a armored Brigade consist of a HHC, A Company, B Company, C Company and if you have enough people then it can go up to D, E, Etc. A, B, & C companys are tanks and thats it. Now the HHC is where your support and Scouts, mortars, medics, and mechanics are at. A HHC usually has double the personel of a tank company.
Platoon-1/ 2 LT
Division-Brigadier Gen or Major General
A Regiment is basically a Brigade, but it has all the components for combat rolled in one small setup similar to a Battalion. In a Armored Cavalry Regiment the Companys are split between Tanks and Bradleys. 1st platoon is tanks, 2nd platoon is bradleys and so forth.
The 82nd Airborne is classified a division because of all the different units that is has. (scouts, mortars, etc.)
Now to help answer your question. It depends on what kind of battalion and to some extent what kind of brigade it is as to what kind of units that you have in it. If you have a Support battalion then it is only medic companys supply companys, mechanic companys, etc. Now if it is a Artillery Battalion, it has platoons of medics, mechanics, support and so on.
The way the bigger units are set up (brigade , division) depends on how many people you have and what kind of unit it is. If it is a combat brigade then you have armor, scouts, mortars, etc that make up most of the unit, with medics, support, mechanics, that make up just a small portion of if.