The problems of multi-energy optimal management and hybrid power flow are investigated to improve the reliability of the energy network. Aiming at multi-energy network constraints and their coupling characteristics, an integrated electricity and heating system is established to integrate multi-energy networks. The fuzzy soft constraint is constructed to quantify the technical dissatisfaction of the networks. A multi-objective optimization scheduling strategy is proposed to minimize the operation cost and technical dissatisfaction of the system with hybrid power flow constraints. An epsilon constraint algorithm is adopted to obtain the Pareto front of the proposed multi-objective optimization problem. Results from the case study indicate that the proposed model and algorithm can effectively improve the quality of energy supply and the accuracy of optimal decisions. It further reflects the benefits of the proposed scheme in the aspects of the economy, quality and complex constraints, as well as ensuring the economical and stable operation of the system.