Integrated energy carriers in the framework of energy hub system (EHS) have an undeniable role in reducing operating costs and increasing energy efficiency as well as the system's reliability. Nowadays, power-to-gas (P2G), as a novel technology, is a great choice to intensify the interdependency between electricity and natural gas networks. The proposed strategy of this study is divided into two parts: (i) a conditional value-at-risk-based stochastic model is presented to determine the optimal day-ahead scheduling of the EHS with the coordinated operating of P2G storage and tri-state compressed air energy storage (CAES) system. The main objective of the proposed strategy is to indicate the positive impact of P2G storage and tri-state CAES on lessening the system uncertainties including electricity market price, power generation of the wind turbine, and even electrical, gas, and thermal demands. (ii) A demand response program focusing on day-ahead load shifting is applied to the multiple electrical loads according to the load's activity schedule. The proposed strategy is successfully applied to an illustrative example and is solved by general algebraic modeling system software. The obtained results validate the proposed strategy by demonstrating the considerable diminution in the operating cost of the EHS by almost 4.5%.