Good spears like ILI, halbs, billmen or other units with good defense stats (especially against mounted units) and/or AP ability are a good match for the non-missile GH cav units. Take the GH cav charge head-on with the spears and flank with the AP units.

The GH HA units are best countered by foot missile units (arbs, xbows and normal bows). If you can place your arbs in an elevated position and protect them with your spears, these guys can really rack up some kills. Pavise arbs/xbows units are especially good in such a missile-unit-shootout.

CMAA units and other 'ordinary' foot units are perhaps not so hot in this scenario.