The use of renewable energy by converting it into heat is an important form of storing energy in a usable form and improving the energy supply flexibility; therefore, the electricity–heating system (EHS) can cope with load fluctuations. However, relevant research is lacking on improving the energy supply limitations by the optimal dispatch of energy flow at the typical EHS, such as the coupled CHP–heat pump–thermal storage system (CCHTS). Based on the study of the energy supply characteristics of the CCHTS for extending the energy supply limitation, this study develops an optimal dispatch method using a heat pump (HP) and the thermal storage (TS) of heating networks to improve the flexibility of the CCHTS and the accommodation capacity of renewable energy. The maximum and minimum energy supply limitation model of the CCHTS and the output power characteristic model are established. Based on the piecewise power supply constraint, the energy flow of the EHS is optimized by using the quadratic programming algorithm. The CCHTS can significantly improve the energy supply flexibility; both coupled combined heat and power (CHP) + HP and coupled CHP + TS can improve the power supply flexibility, but the enhanced effect of CHP + HP is better than that of CHP + TS. An increase of 7.6% in wind power consumption is achieved. The consumption of renewable energy increases by 17.9% in the energy flow optimization results.