Has this changed? My last flight I was allowed 1 actual carryon and a personal item that would fit under the seat in front of me. That was American Airlines and British Airlines.
I think it is termed as a carry-on and a personal item. I usually fly with my LL Bean backpack and a rolling carry-on that is typical US size (and is only slightly smaller than my checked suitcase). Never had any problem on a US airline, though I do generally have to gate-check the rolling carry-on on my connecting flight. Backpack goes under the seat in smaller planes.
When I flew last month, I flew Virgin and also had two carry-ons, though not my rolling one. Again, had no issues. YMMV but I have never been on an international flight where the larger carry-ons were not accepted.