US army totaled 91 Divisions and the Marines had 6.
68 Infantry
16 Armored
6 Marine
5 Airborne
2 Cavalry
1 Mountain
One infantry division was disbanded after its loss in the Philippines.
One cavalry division was disbanded to provide service troops. The other fought as infantry. So:
68 or 69 Infantry
16 Armored
6 Marine
5 Airborne
1 Mountain
Armored divisions had 2 tank regiments, 1 armored infantry, and 1 artillery. The rest had 3 infantry/specialist infantry regiments and 1 artillery regiment. The 1st cavalry technically had 4 dismounted cavalry regiments, but each one only had 2 battalions, leaving the division with only 8 rifle battalions.
Plus 63 or so tank destroyer battalions and the corps artillery battalions.
Edit: It might be easier to model the independent units by attaching a TD battalion to every regular infantry division and buffing the divisional artillery with an additional battalion or two
When you say "regiment" you mean "4-5 battalions of the same type together" right? Or just 3 battalions?