A High-Altitude Pseudo-Satellite (HAPS) is a fixed-wing, solar-powered Unmanned Aerial Vehicle (UAV) developed to become a flexible alternative to satellites with fixed-orbits for monitoring ground activities over long periods of time. However, given its lightweight build and weak electro-motors, the platform is rather sensitive to weather and cannot fly around hazardous weather zones swiftly. In this work, we formulate the problem of planning missions for multiple HAPS as a hybrid planning problem expressed in PDDL+. The formulation also considers the problem of modeling the platform dynamics, the time-varying environment, and the heterogeneous tasks that need to be carried out. Additionally, we propose a framework that combines a PDDL+ automated planner with an Adaptive Large Neighborhood Search (ALNS) approach, developed to couple the automated planner with a meta-heuristic that is specific for the problem. The task and motion planning are done in an intertwined way within the framework, preserving hence a common decision/search space. We validate our approach with a third-party realistic simulator for HAPS, as well as with a set of benchmark tests, showing that our integrated approach produces executable mission plans.