The rising energy demand and the imperative to reduce carbon emissions have underscored the need for developing integrated energy systems capable of coordinating multiple energy carriers. This study presents an integrated optimization model for the operational coordination of gas and electricity networks, enabling bidirectional energy exchange between these networks through combined heat and power (CHP) units and power-to-gas (P2G) technologies. The proposed model incorporates renewable energy sources (wind and solar), battery storage systems, and electric vehicles as flexible components within the electricity network. By considering the technical constraints of both networks, the model simultaneously aims to optimize operational costs and reduce emissions. The objective function minimizes the total costs associated with energy procurement, operation of CHP and P2G units, and carbon emission penalties. Key constraints include power balance in the electricity network, gas flow balance, battery charging/discharging dynamics, electric vehicle charging patterns, and energy conversion capacities of CHP and P2G units. Simulation results on a case study demonstrate that the proposed model achieves up to an 18% reduction in operational costs and a 25% decrease in carbon emissions compared to non-integrated models by leveraging intelligent energy exchange between networks. This framework offers an efficient tool for network operators to manage distributed resources and enhance the sustainability of the energy system.