This paper describes the development, implementation and experimental investigation of a Hybrid Model Predictive Control (HMPC) strategy to control solar-assisted heating, ventilation and air-conditioning (HVAC) systems with on-site thermal energy generation and storage. A comprehensive approach to the thermal energy management of a residential building is presented to optimise the scheduling of the available thermal energy resources to meet a comfort objective. The system has a hybrid nature with both continuous variables and discrete, logic-driven operating modes. The proposed control strategy is organized in two hierarchical levels. At the high-level, an HMPC controller with a 24-h prediction horizon and a 1-h control step is used to select the operating mode of the HVAC system. At the low-level, each operating mode is optimised using a 1-h rolling prediction horizon with a 5-min control step. The proposed control strategy has been practically implemented on the Building Management and Control System (BMCS) of a Net Zero-Energy Solar Decathlon house. This house features a sophisticated HVAC system comprising of an air-based photovoltaic thermal (PVT) collector and a phase change material (PCM) thermal storage integrated with the air-handling unit (AHU) of a ducted reverse-cycle heat pump system. The simulation and experimental results demonstrated the high performance achievable using an HMPC approach to optimising complex multimode HVAC systems in residential buildings, illustrating efficient selection of the appropriate operating modes to optimally manage thermal energy of the house.