Clean heating is a powerful solution for satisfying the building heat demand by synergizing energy efficiency and carbon emission. For satisfying the newly increased heat load, this paper constructs an alternative integrated electricity and heat energy system (IEHES) to consider different clean heating supply modes, namely electrical-heating mode (EH, electric boiler or electric heat pump), CHP unit with high back-pressure turbine heating mode (HBP–CHP), and auxiliary heat source heating mode (AHS, coal-fired boiler or gas-fired boiler). An optimal configuration planning and dispatch model is proposed for comparing the performance of the three heating modes. Wherein, a new comprehensive energy-carbon price is proposed as the optimization objective to minimize this system's total production costs and carbon emission costs. The results show that the HBP-CHP mode is the optimal solution when the heat load growth rate λ is lower than 14%, followed by the electric heat pump heating way under the EH mode. However, the HBP-CHP mode will limit the flexibility of the IEHES when λ is larger than 8%. Therefore, we propose a combined heating mode by introducing the electric heat pump into the HBP-CHP heating mode that facilitates the flexibility of the IEHES and brings the optimal system coal-saving effect.