This paper analyses optimal electricity investments (PV and battery storage) to decarbonise heat supply in residential buildings under different heat pump and energy retrofitting scenarios in a detailed representation of the Swiss power and heating system. The sensitivity of PV and storage deployment, including lithium-ion (LiB) and vanadium redox flow batteries (VRFB), with respect to distribution network capacity is also investigated. We propose an open-source dispatch sector coupling model (GRIMSEL-AH) to minimise energy system costs (social planner perspective) for heating and electricity supply in Switzerland with hourly and daily time resolution for electricity and heating respectively. Moreover, our representation of the Swiss energy system includes various types of consumers and urban settings which are represented with monitored electricity demand data for each sector and simulated heat demand data at the building level for the residential sector. We find that under a “business as usual” heat pump deployment and retrofitting rate, the optimal electricity investments correspond to 27.8 GWp of PV combined with 16.9 GW (33.8 GWh) for LiB and 1.9 GW (7.6 GWh) for VRFB. For this case, 57% (13.3 TWth/year) of the residential heat demand is covered by heat pumps with a total installed capacity of 19.7 GWth by 2050 (capacity exogenously set with its operation optimised). With increasing heat pump deployment, retrofitting rates are found to have a large impact on the investment in storage and a 100% heat pump scenario for the residential sector appears to be feasible. Our results show that heat pumps do not only decarbonise heat but also provide extra flexibility to the power system, since they increase local PV self-consumption, resulting in higher PV deployment. The model and the methodology presented in this study can be applied to other countries.