In this paper, optimal scheduling for multi-energy service providers (MESPs) to participate in the Integrated power and natural gas market (IPNGM) and the allocation of power and natural gas for MESs is presented. In the proposed model, MESPs intend to minimize the cost of purchasing power and natural gas via implementing the energy storage systems and the demand response program (DRP). MESPs benefit from a unit commitment problem constrained to integrated electricity and natural gas networks (IENGN) by considering the flexibility of the line pack system. Also, to investigate the counter effect of flexible energy sources and IPNGM, an iterative-based two-step algorithm is taken into account. Since MESPs cannot accurately predict other participants in the IPNGM, especially renewable energy sources (RESs), the electricityprice determined by IPNGM is considered an uncertain parameter. To this end, a robust optimization (RO) method is employed to deal with the wholesale electricity market intermittency. power system integrated with the 6-node natural gas network and considering one MES. Furthermore, to show the model flexibility, simulation results are extended to the IEEE 118-bus power system integrated with the 10-node natural gas network by considering six MESs. Obtained results demonstrate that MESPs can reduce the cost of the purchased electricity and natural gas up to 4.39% by employing flexible energy sources.