With the introduction of China's dual carbon target, the low-carbon energy system transformation faces many risk challenges. The integrated electricity and heating system planning plays a key role in the low-carbon transformation of the energy system. The current research related to the integrated electricity and heating system planning considering the energy policies is not complete in the planning candidate equipment consideration, and many planning studies of the integrated energy system only consider the thermal power balance for the thermal system. The thermal network model in energy systems planning is not accurate enough. For this reason, this paper considers the low-carbon policies as well as the variable flow and the variable temperature strategy of the hydraulic-thermal heating network modeling. An integrated energy system planning model including combined heat and power units, electric boilers, heat storage tanks, transmission lines, and thermal pipelines is established. For the non-convex nonlinear hydraulic-thermal heating network model, the quadratic convex relaxation algorithm is used to transform the planning model into a mixed integer second-order cone programming model. The effectiveness of the proposed method is also verified by the simulation analysis.