Multi-connectivity (MC) with multi-RAT (Radio Access Technology) can be used to enhance data throughput and reliability of wireless communication systems. A Korea-EU joint research named 5G-ALLSTAR has been pursuing a variety of service scenarios with multi-connectivity, and service continuity is one of the most important ones to be proven. The multi-RAT in the 5G-ALLSTAR is comprised of a mmWave-based 5G cellular access network and a satellite access network. We integrated these systems into an MC testbed and validated it to prove the concept and the feasibility of the service continuity. Specifically, we focused on the demonstration of video streaming services which the service continuity can be clearly verified with. To aggregate the data traffic of each RAT, an IP layer traffic controller has been adopted. Testing with the integrated MC testbed showcased the concept of the service continuity successfully.