In Africa the Karthagians used thousands of chariots, at least they had the stables for these numbers in the city. Of course, like every other polis around the Mediterr she had the militia forces (probably armed like Greek Hoplites). To this came allied forces, for example the levy of subjugated Numidian and Spanish tribes. And then in a growing numbers local mercenaries.

If you like, the armed forces of Karthago were the exact opposite of the Roman army: while the Romans payed much effords in uniformation, hardly two Karthagian armies would have looked the same.