In most studies about operation optimization of integrated energy system (IES), the heating subsystem adopts the quality regulation method. However, considering the poor economy of quality regulation, quantity regulation method is proposed to improve the economy. Due to possible hydraulic vertical imbalance resulted from quantity regulation, the operation optimization must consider the effects of both thermal and hydraulic dynamic characteristics on IES. In this work, a new multi-objective quantity regulation scheduling method of electric-thermal IES is proposed, which adopts an electro-thermal decoupling bi-level optimization structure, a nonlinear dynamic thermo-hydraulic network model, objectives of economy and carbon emission indices and more reasonable nonlinear constraints. An IES prototype of 5-node power system with 5-node thermal system is designed to verify the proposed quantity regulation scheduling method. When solving the optimization problem, method NSGA-II combines with Gurobi is 40% faster in computational speed when compared with other methods. When compared with a single layer solution method, the proposed bi-level optimization model results in a scheduling strategy that can absorb 100% renewable power with operation cost of 10150.18 U.S. dollars (39.5% reduction) and carbon emission of 1303.7 ton (13% reduction). The hydraulic transient process resulted from the quantity regulation is also analyzed to demonstrate that the optimized scheduling strategy could satisfy the safety requirement of the heating network operation. Therefore, the proposed scheduling optimization method is more effective and satisfied.