With the acceleration of the energy transition process, the Electricity-Gas-Heat Interconnection System (EGHIS) has become a key carrier for improving energy utilization efficiency owing to its multi-energy complementary characteristics. However, the heterogeneous energy coupling problem existing in the interconnection system leads to low utilization rates of various energy sources and poor transmission security, which has an impact on the stability of the system. Therefore, in this paper, for the multi-energy flow coupling characteristics and safe operation requirements in the EGHIS, an economic optimal scheduling method for the EGHIS considering safety indicators is proposed. By constructing a multi-energy flow coordinated optimization model that takes into account safety margin, safety balance equation and safety constraints, the collaborative improvement of the economic operation and safety of the system is achieved. The effectiveness of this method was verified through the system simulation of YALMIP and CPLEX. Compared with the adoption of traditional methods, the line blocking rate is reduced by 33%, and the multi-energy coordinated dispatching reduces the operating cost of the power system by 34.69%. The research results show that through the collaborative optimization of safety constraints and economic goals, the balance problem between “ensuring supply” and “increasing efficiency” in the EGHIS can be effectively solved.