The need for innovative heating and cooling systems to decarbonize the building sector is widely recognized. It is especially important to increase the share of renewables at building level by maximizing self-consumption and reducing the primary energy demand. Accordingly, in the present paper, the results on a wide experimental campaign on a hybrid system are discussed. The system included a sorption module working as the topping cycle in a cascade configuration with a DC-driven vapor compression heat pump. A three-fluids heat exchanger with a phase change material (PCM), i.e., RT4 with nominal melting temperature of 4 °C, was installed on the evaporator side of the heat pump, for simultaneous operation as thermal storage and heat pumping purposes. The heat pump was connected to a DC-bus that included PV connection and electricity storage (batteries). Results showed that the energy efficiency of the heat pump in cascade operation was double compared to compression-only configuration and that, when simultaneously charging and discharging the latent storage in cascade configuration, no penalization in terms of efficiency compared to the compression-only configuration was measured. The self-sufficiency of the system was evaluated for three reference weeks in summer conditions of Athens climate and it was found that up to 100% of the electricity needed to drive the system could be self-produced for a modest cooling demand and up to 67% for the warmer conditions with high cooling demand.