Industrial parks (IPs) play a crucial role in facilitating economic efficiency and comprehensive energy utilization in the industrial age. At the same time, multi-energy coupling and management of various types of energy in IP have become serious challenges. In this paper, combined heat and power unit (CHP) model considering operation mode switching characteristics is formulated by exploring its internal composition to improve output flexibility of the energy supply side. Then, heat and electricity integrated energy system (HE-IES) optimal dispatch and pricing model are established, taking electricity and heat demand response strategy and steam thermal inertia property into account. Based on the above models, a mixed-integer bilinear programming framework is designed to coordinate the day-ahead operation and pricing strategy of the HE-IES in the IP. The scenario study is carried out on a practical industrial park in Southern China. Numerical results indicate the proposed mechanism can effectively improve IP’s energy utilization and economic efficiency.