Also, what of the two kinds of infantry?
Personally, the way A&A is set-up, having two or more infantry is not practical.
Commando units for example did not operate in Division size units. At the most they were no bigger than than several brigades in size. Also, commando units in WWII were created to perform a specific task. These special tasks are harder to integrate such units on a large Strategic game like A&A. However, these unit might find some use in games like D-Day and Guadalcanal which are much closer to a tactical game.
Now there were specialized infantry divisions such as Airborne, SS, Russian shock Troops and to a lesser extent Marines (But I personally wouldn’t classify them as such. They are simply a naval infantry). So if such unit were created then they should have some limited specialized ability. Airborne can be transported by plane, SS have a special attack or defense against armor, Russian shock troops get a +1 attack on the first assault, Marine get a +1 attack on the first wave of a beach attack and so on.
Now, if you create such units they should obviously cost more. However, now you run into another problem, cost. If infantry is 3 IPCs, Mech Infantry-4 and Armor-5. Where does that leave special infantry? The most logical choice would be 4 IPC but in most cases the mech infantry will be superior to these special infantry divisions. With this in mind, the only unit I see of any value under these condition would be Airborne divisions if they are allowed to move underspecial conditions without using aircraft unit (I would assume that airborne divisions would included aircraft for transportation).