With the development of economy and the growth of industrial demands, the peak-valley difference of electric load is ever increasing, calling for the deployment of energy storage units. Advanced-adiabatic compressed air energy storage (AA-CAES) is a promising large-scale energy storage technology and exhibits various advantages in fast response, long service time, low environmental impact and so on. It also has the potential in combined heat-and-power production because heat is a by-product when air is compressed. This study presents a novel AA-CAES-based energy hub and its mathematical formulation considering the pressure behaviours and mass flow rate variations of AA-CAES, and further envisions its business model for the transaction with a power distribution system and a heating system under time-of-use price. A bilevel game-theoretical model is developed to capture the interaction between the two infrastructures through the integrated demand response of the energy hub and investigate the equilibrium state at which none of the stakeholders would like to alter their strategy unilaterally. Results show the interdependence of electricity and heat prices as well as the economic impact of energy hub performance.