The choice of the transmitting frequency to provide cellular-connected Unmanned Aerial Vehicle (UAV) reliable connectivity and mobility support introduce several challenges. Conventional sub-6 GHz networks are optimized for ground Users (UEs). Operating at the millimeter Wave (mmWave) band would provide high-capacity but highly intermittent links. To reach the destination while minimizing a weighted function of traveling time and number of radio failures, we propose in this paper a UAV joint trajectory and band switch approach. By leveraging Double Deep Q-Learning we develop two different approaches to learn a trajectory besides managing the band switch. A first blind approach switches the band along the trajectory anytime the UAV-UE throughput is below a predefined threshold. In addition, we propose a smart approach for simultaneous learning-based path planning of UAV and band switch. The two approaches are compared with an optimal band switch strategy in terms of radio failure and band switches for different thresholds. Results reveal that the smart approach is able in a high threshold regime to reduce the number of radio failures and band switches while reaching the desired destination.