[serg3d]

Second russian-chechen war was fought mostly with recce, spetznaz and artillery/CAS. Modus operandy was - recce or int were locating insurents groups, spetznas or other recce were fixing it in plase and CAS/arty doing the killing. Assault on the prepared insurgent positions was not often - mostly it was cat and mouse game. Armor and line ifantry were used mostly for occupation and mopping up operations. From other hand for chechens, in urban comabt main unit were weapon squad - one MG, one sniper and/or infantry-AT and one-two AK. Chechen used a lot of vehicles - common civilian cars, that gave them quite high mobility. They used tanks only in the first war AFAIK, but not attached to battalions, they concentrated them in company strength and used under command of their HQ(in Grozny). Havn't read anything about use of ATGM. Chechens hadn't used any inderect arty, but used a lot of indirect mortars.

So for contrinsurgency based on the chechen-like war I'd say
realistic mix would be :

For government - incompetent leadership(like first chechen war): classical mix of forces, as Mobhack recommend, or even armor without infantry. Or low quality infantry.

for government (more competent leadership like second chechen war):
A lot of arty/CAS, a lot of recce and different kinds of special forces, some armor/SPA and infantry - could be mix of different type as they are attached from different units to this area/operation.

For insurgent/separatist: If it is a first stage of government invasion - some armor, no air units, no artillery/MRL, lot of mortars, lot of highly-trained weapon squads with utility vehicles, militia, infantry-SAM. In the cource of war amount of armor, vehicles and weapon sqauds should be gradually reduced in favor of militia and mercenaries/mojaheds.