The integrated electricity and heating system (IEHS) can satisfy the diversified energy demand and improve energy efficiency through electro-thermal synergy and complementarity, which is beneficial for energy transformation and global climate governance. To reduce the operation cost, renewable energy source (RES) abandonment, and purchased electricity of IEHS, an optimal dispatching method of IEHS with multiple functional areas considering the flow regulation of the heat network is proposed. Firstly, the functional area of IEHS is classified and the functional area’s load characteristics are analyzed. Secondly, a heat network model considering refined resistance and dynamic characteristics is constructed and the operation regulation modes of the heat network are analyzed. Thirdly, an optimal dispatching model of IEHS with multiple functional areas considering heat network flow regulation is established to minimize the operation cost of IEHS with multiple functional areas while considering the penalty cost of RES abandonment and time-of-use electricity price. Finally, a certain region in China is taken as a case study to verify the effectiveness of the proposed optimal dispatching model. The case study shows that the quality regulation mode of the heat network considering flow change in multiple stages can effectively reduce RES abandonment by 2.4%, purchased electricity by 5.4%, and the system operation cost by 1.7%. In addition, compared with the independent dispatching of each functional area, the joint dispatching of IEHS with multiple functional areas can reduce the amount of RES abandonment by 95.2% and purchased electricity by 66.5%, and lower the operation cost of IEHS by 23.6%.