Accessing and interacting with difficult to reach surfaces at various orientations is of interest within a variety of industrial contexts. Thus far, the predominant robotic solution to such a problem has been to leverage the maneuverability of a fully actuated, omnidirectional aerial manipulator. Such an approach, however, requires a specialised system with a high relative degree of complexity, thus reducing platform endurance and real-world applicability. The work here presents a new aerial system composed of a parallel manipulator and conventional, underactuated multirotor flying base to demonstrate interaction with vertical and non-vertical surfaces. Our solution enables compliance to external disturbance on both subsystems, the manipulator and flying base, independently with a goal of improved overall system performance when interacting with surfaces. To achieve this behaviour, an admittance control strategy is implemented on various layers of the flying base's dynamics together with torque limits imposed on the manipulator actuators. Experimental evaluations show that the proposed system is compliant to external perturbations while allowing for differing interaction behaviours as compliance parameters of each subsystem are altered. Such capabilities enable an adjustable form of dexterity in completing sensor installation, inspection and aerial physical interaction tasks. A video of our system interacting with various surfaces can be found here: https://youtu.be/38neGb8-lXg .