To take out armoured horse-archers use slingers. Pantodapoi Phalangitai have axes too, so use them as main melee infantry. Don't use Pantodapoi, skirmishers, parthian spearmen or eastern axemen, they don't have enough armor. In Antiocheia-Margiane you can get Dahae Riders (the horse-archers, not the skirmisher cavalry) which are also pretty good to fight other horse-archers, in Asaak and Hekatompylos you get parthian horse-archers.
With about 6-7 pantodapoi phalangitai and lots of missile units (don't forget the slingers) you should be able to defend yourself. You don't reallly need heavier troops if you have enough pantodapoi phalangitai.
Before you get Katas your best cavalry to counter the Parthians would probably be Prodomoi, all cavalry you get in the East (except for the Kinsmen) is no match for the armoured parthian units.
Oops, ARCHIPPOS was faster - I agree to what he says.
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