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The Armoured/Light Cavalry are part of Mixed combat brigades.
There are three Brigades with the same structure.

Brigade Headquarters
An Armoured/Light Calvary regiment
A Mechanised Infantry Battalion(from the Royal Australian Regiment)
A Motorised Infantry battalion(from the Royal Australian Regiment) 
An Artillery Regiment
A combat Engineer Regiment
A combat Signal regiment
And a combat service support Regiment.

The one Light Infantry/Amphibious battalion is part of a separate unit entirely that is for amphibious warfare.

> The last point makes me wonder why the armoured/light horse regiments mix tracked and wheeled vehicles. Clearly those APCs aren't just for recon, since they're in a 2:1 ration to tanks, and yet following tanks on roads wastes their superior mobility and they can't follow in some difficult terrains. Why not mix M113s and Abrams? 

They were mixed with M113s until they gave them away to the Infantry to rerole them as Mechanised Infantry. I think they may be largely for recon as well, because of the mixed combat brigade nature of the deployment. The infantry battalions consist of three rifle companies, a support company, logistics company and headquarters. I tried to find the exact composition of these units but I could not, however by this composition it seems they may not have that much organic recon(but I can't say for sure). Our reserve cavalry regiments specialise in recon as well(but in light vehicles) which maybe hints at a recon role for the cavalry regements in general. Plus wheeled vehicles are probably good for the dry plains that cover much of Australia.

Also as a side note we are replacing the ASLAVS in the Armoured/Light Cav divisions with Boxers(but they are wheeled too). And the M113s in the mechanised infantry are being replaced by either Lynxs or Haniwa Redbacks(it's an ongoing competition).