Human-robot interaction will play an essential role in various industries and daily tasks, enabling robots to effectively collaborate with humans and reduce their physical workload. Most of the existing approaches for physical human-robot interaction focus on collaboration between a human and a single ground or aerial robot. In recent years, very little progress has been made in this research area when considering multiple aerial robots, which offer increased versatility and mobility. This paper proposes a novel approach for physical human-robot collaborative transportation and manipulation of a cable-suspended payload with multiple aerial robots. The proposed method enables smooth and intuitive interaction between the transported objects and a human worker. In the same time, we consider distance constraints during the operations by exploiting the internal redundancy of the multi-robot transportation system. The key elements of our approach are (a) a collaborative payload external wrench estimator that does not rely on any force sensor; (b) a 6D admittance controller for human-aerial-robot collaborative transportation and manipulation; (c) a human-aware force distribution that exploits the internal system redundancy to guarantee the execution of additional tasks such inter-human-robot separation without affecting the payload trajectory tracking or quality of interaction. We validate the approach through extensive simulation and real-world experiments. These include scenarios where the robot team assists the human in transporting and manipulating a load, or where the human helps the robot team navigate the environment. We experimentally demonstrate for the first time, to the best of our knowledge, that our approach enables a quadrotor team to physically collaborate with a human in manipulating a payload in all 6 DoF in collaborative human-robot transportation and manipulation tasks.