Multi-carrier energy systems (MCESs) can be formed by the integration of various energy infrastructures including power and natural gas systems. The proliferation of bidirectional energy conversion units in an MCES can set the stage for a more resilient and robust system. This study shows how bidirectional energy conversion units and storage devices can be optimally scheduled within an MCES for provision of various regulation services to the grid operator. To that end, a new model is proposed for optimal scheduling of power-togas (PtG), gas-fired generation, and gas storage units in an MCES. The model aims to facilitate integration of renewables, utilise gas, and power price arbitrage, provide regulation services to the real-time (RT) market, and contribute to the system restoration. New indices that quantify the contribution of the MCES operator to RT and ancillary service markets are proposed. The proposed model is validated technically and economically by using a test system historical operating data. Numerical results demonstrate that while the proposed model is technically feasible, it also enhances the economic viability of the grid operator.