Judging by the number of casualties, the number of Military present in Pripyat, it seems each helicopter likely carried around 12 men, for a total of 60 - 4 crew, and 8 soldiers, the same amount that the MI-24 is originally designed to carry. Though STINGRAY helicopters are obviously Hind's, they have been specially modified with emission-resistant systems and countermeasures for the Zone's various threats. They have the same design as the MI-24 'Hind' gunship, a common Soviet assault/transport helicopter that is still used today.
Their design was seemingly foolproof and not a single helicopter was to be lost - instead, as the intro to Call of Pripyat shows, every single one was either shot down or grounded due to the unknown causes, stranding most of the military if not killing them outright, forcing them to fall back to evacuation zones throughout the area. The high-tech helicopters were designed to traverse the Zone's normally dangerous air in order to deliver a large battalion of soldiers into the heart of Pripyat itself, in order to make a move to retake the Chernobyl NPP from the hands of Monolith.