The required decarbonization of the energy system is a complex task, with ambitious targets under the Paris Agreement, and related policy analysis should consider possible impacts on the economy and society. By coupling the energy system model TIMES PanEU with the impact assessment model EcoSense and the computable general equilibrium model NEWAGE, we present an integrated assessment toolbox for the European energy system capable of internalizing health damage costs of air pollution while simultaneously accounting for demand changes in energy services caused by economic feedback loops. The effects of each coupling step are investigated in a scenario analysis. Additionally, CO₂ decomposition analysis is applied to identify the main drivers to decarbonize the energy system. Our results show that integrating externalities forces the system to take early action, which provides benefits on the societal level. Including macro-economic variables has a negative effect on energy service demands and generally reduces the need for structural change, which are still the main drivers of decarbonization. The tighter the models are coupled, the fewer the iterations needed and the lower the CO₂ prices resulting from the carbon cap and trade system. In this aspect, an integrated view can provide valuable insights to determine efficient and effective decarbonization paths.