Electric vehicles and heat pumps are pivotal in decarbonizing transport and heat, while their demand-side flexibility can further support integration of high shares of renewable generation. This study aims to assesses the complementarity of demand-side flexibility by electric vehicles and heat pumps in the Swiss electricity system in 2050. Electricity system modeling at high spatial and temporal resolution is used to compare uncontrolled charging, controlled charging, and vehicle-to-grid for electric vehicles, as well as uncontrolled and controlled operation for heat pumps. The results demonstrate that flexibility provided by electric vehicles and heat pumps together can enhance renewable electricity integration and correspondingly decrease electricity import to Switzerland, especially during winter months. This combined flexibility can reduce the need for installing battery storage too. However, synergetic effects between electric vehicles and heat pumps on battery utilization, solar generation and import only emerge under three conditions: in the absence of high renewable shares already, with restrictions on cross-border trading, and with vehicle-to-grid technology. The impact of heat pump flexibility on renewable integration and storage displacement is less pronounced than that of electric vehicles.