This paper considers the problem of performing bimanual aerial manipulation tasks in grabbing conditions, with one of the arms grabbed to a fixed point (grabbing arm) while the other conducts the task (operation arm). The goal was to evaluate the positioning accuracy of the aerial platform and the end effector when the grabbing arm is used as position sensor, as well as to analyze the behavior of the robot during the aerial physical interaction on flight. The paper proposed a control scheme that exploits the information provided by the joint sensors of the grabbing arm for estimating the relative position of the aerial platform w.r.t. (with respect to) the grabbing point. A deflection-based Cartesian impedance control was designed for the compliant arm, allowing the generation of forces that help the aerial platform to maintain the reference position when it is disturbed due to external forces. The proposed methods were validated in an indoor testbed with a lightweight and compliant dual arm aerial manipulation robot.