but the 2nd and 3rd where 'old' heavy divisions that used a very different TO/E.
Initially their two regiments consisted of one light battalion (three companies of light tanks) and two medium battalions (each with three medium companies). Later these were mixed because the light battalion had too little power. These companies kept their names which resulted in unusual combinations of companies in the battalions.
The regular/light Armored Divisions had three battalions as described by you, but that does not apply to the 2nd and 3rd AD in the ETO (and 1st in the MTO IIRC).