Halberds are in fact militia kinda-guys, except the swiss. Billmen, don't know, but I think it's in fact still peasant class, though (as many other English unit types were) probably very well trained and led. Not that it matters really, but in the game it is represented by morale stats. The Halberd bearing units (except the swiss) bear, IIRC, low morale stats. Of course, Halberds and pikemen became (even more than crossbowmen, longbowmen and firearms) the scourge of Knights, being lower class and low trained, so plentifull in supply.
However, as much as you blow the horn of praise about them halberds here, as much as I believe that is the most independent and versatile unit in the field, I believe a well executed attack at these troops by high quality swordsmen, combined if possible with heavy cav and preluded by firearms fire (or other armour piercing things) will break them in any way. CMAA, VG, CFK or even heavy Carls will make short work of them, preferrably in wedge, because when the attack is executed probably, the low morale of the defender will be their doom.

But if you hadn't noticed, my favorite tactic involves anything with swords and axes, accompanied with Heavy or Medium Cav. I Like all aspects and units of this game, especially the mix, but any decend attack has heavy cav and swords, else no fun!