There have been increasing interests in applying Software Defined Networking (SDN) to aeronautical communications primarily for air traffic management purposes. From the service passenger communications' point of view, a major goal is to improve passengers' perception of quality of experience on the infotainment services being provided for them. Due to the high speed of aircrafts and the use of multiple radio technologies during different flight phases and across different areas, vertical handovers between these different radio technologies are envisaged. This poses a challenge to maintain the quality of service during such handovers, especially for high bandwidth applications such as video streaming. This paper proposes an SDN-based aeronautical communications architecture consisting of both satellite and terrestrial-based radio technology. In addition, an experimental implementation of the Locator ID Separation Protocol (LISP) protocol with built-in multi-homing capability over the SDN-based architecture was proposed to handle vertical handovers between the satellite and other radio technologies onboard the aircraft. By using both objective and subjective Quality of Experience (QoE) metrics, the simulation experiments show the benefit of combining LISP with SDN to improve the video streaming quality during the handover in the aeronautical communication environment.