Renewable sources will play a key role in meeting the EU targets for 2030. The combined use of an aerothermal source through a heat pump and a solar source with a photovoltaic (PV) system is one feasible and promising technology for the heating and cooling of residential spaces. In this study, a detailed model of a single-family house with an air-source heat pump and a PV system is developed with the TRNSYS simulation software. Yearly simulations are run for two types of buildings and nine European climates, for both heating and cooling (where needed), in order to have an overview of the system behaviour, which is deeply influenced by the climate. The storage system (electrical and thermal) is also investigated, by means of multiple simulation scenarios, with and without the battery and with different water storage sizes. The numerical results provide an overview of the performance of the considered heating and cooling system, as well as the balance of the electrical energy exchange between the grid, the building, and the PV array.