The increasing penetration of renewable energy sources introduces higher requirements for the operation flexibility of transmission system (TS) and connected active distribution systems (DSs). This paper presents an efficient distributed framework for the TS and DSs to work cooperatively yet independently. In addition to conventional power interaction, upward and downward reserve capacities are exchanged to form the feasible access regions at the boundaries that apply to different system operation situations. A distributed robust energy and reserve dispatch approach is proposed under this framework. The approach utilizes the supply- and demand-side resources in different systems to handle various uncertainties and improve overall efficiency and reliability. In particular, integrated as aggregated virtual energy storage (AVES) devices, air-conditioning loads are incorporated into the optimal dispatch. In addition, a reserve model with charging/discharging-state elasticity is developed for AVESs to enhance system flexibility and provide additional reserve support. Different cases are compared to verify the effectiveness and superiority of the proposed approach.