Coordinating the interactions between increasingly interconnected energy sectors and carriers can lead to an efficient integration of variable renewable energy (VRE) resources, and a more cost-efficient energy transition. This paper proposes a model coupling approach that uses a market-based mechanism to efficiently coordinate the interactions among electricity, heat, and (hydrogen) gas systems, and (near) optimally schedule flexibility to maximize social welfare. The proposed approach is benchmarked against traditional co-optimization, and is shown to achieve comparable results with a moderate "optimality gap"in terms of reduction in system costs, peak load, and VRE curtailment. Its added value is the ability to enable each system to interact in an integrated energy system and locally optimize their decisions without sharing confidential information. The practical implication of this new approach is to provide a modeling environment where system operators and flexibility aggregators can obtain insights into the impacts of decarbonization of other parties on their systems - thereby avoiding myopic operational or investment decisions.