Advanced adiabatic compressed air energy storage (AA-CAES) is a promising form of CAES technology, which can realize multi-energy cascade storage and supply. Given the characteristics of cooling, heating, and power (CHP) load demand of regionally integrated energy system (IES) and the overall need to control the total carbon emission, this study first establishes the AA-CAES multi-energy storage model; second, based on analyzing the multi-energy characteristics of AA-CAES, a ladder-type carbon trading mechanism is introduced; furthermore, aiming for minimal system operating costs and carbon trading costs, an optimal dispatch model of an integrated energy system with AA-CAES as the energy hub for coupling multiple energy forms is established. Finally, an empirical study was conducted based on the energy use scenario of a provincial and ministerial university in Qinghai Province. This study analyzes the impact of the operation of AA-CAES and the introduction of ladder-type carbon trading on the operating costs and carbon trading costs of IES. The simulation results show that the total operating cost of the proposed model is reduced by 23.9%, and carbon emission is decreased by 14.5% compared to the conventional IES. It proves the validity of coupling AA-CAES and stepped carbon trading mechanisms to facilitate low-carbon economy in IES.