In addition to heavy shock chariots and light missile chariots, chariots also performed the function of battle taxis: carrying warrior champions into battle and retrieving them (or saving them if wounded).
Very popular during the Homeric Age.
Combining missile and melee capabilities probably makes this transport chariot closer to cavalry, with light chariots using shoot-and-scoot missile tactics are frankly analogous to light horse.
Which leaves us with
Knights = heavy chariots Cavalry = transport chariots Light Horse = light chariots
Basically, this new unit would be a chariot version of mtd-x with the dismounted unit being treated as a blade.