Multi-vehicle aerial robots present great potential in accomplishing manipulation tasks, because of their high payload capacity and full manipulability in 3-dimensional space. Belonging to this class of aerial robots, the Flying Parallel Robot (FPR) is an architecture where a moving platform is supported collectively by a team of quadrotors with passive kinematic chains. While the modelling and control of the FPR in free space has been studied in the previous work, there is lack of consideration in robot-environment interaction, which is however significant to develop the industrial applications of such robots. In this paper, we implement an external wrench estimator and an impedance-based controller with force tracking capability to achieve the disturbance rejection and the physical interaction with the environment. Extensive experimental validations have shown the FPR capable of hovering in presence of additional payload and strong wind perturbations, and performing contact-based interaction tasks.