In this paper, we present a model predictive controller for a fully actuated aerial manipulator to track a hybrid force and pose trajectory at the end-effector in an aerial interaction task. A force sensor at the end-effector is used to detect contact and to directly control the interaction force. We propose an approach for automatic transition between three operation modes which reflect the state of contact constraints, including free flight and two modes for force control based on static or dynamic friction at the end-effector. This division into three modes allows for different mode-specific controller tunings to optimize the desired performance throughout an interaction task. Results from flight experiments which combine force, position, and attitude tracking, show the performance of the controller in terms of accuracy and precision. The performance is further benchmarked against a hybrid force/impedance controller.