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Ignoring reserve, artillery and support units, The Australian army has two armoured regiments and a light horse regiment that each consist of two cavalry Squadrons(with ASLAVs) and a tank squadron(with Abrams). I don't know how big a squadron is but considering the Australian army only has 50 Abrams it cannot be that big.
We also have the Royal Australian Regiment which consists of three mechanised infantry battalions(M113s, three motorised infantry battalions and an amphibious/light infantry battalion.
It's pretty descriptive I think.
I think armoured infantry is a fine description too, kind of like PanzerGrenadiers. Armoured cavalry is kind of strange, unless you have unarmoured calvary too.