This paper proposes a new distributed dispatch scheme to realize efficient coordinated real-time dispatch of the coupled transmission grid and active distribution grids (ADGs). In the proposed scheme, on the one hand, the concept of optimal power exchange interval is introduced to coordinate the transmission grid and ADGs so that the reserve capacity support from ADGs can be incorporated in the dispatch optimization of the transmission grid. On the other hand, uncertainties of renewable distributions are considered to ensure the robustness of dispatch decisions. With the analytical target cascading (ATC) method, the centralized distributionally robust dispatch model for the integrated transmission-distribution system is decoupled, leading to a number of independent small local optimization problems for the transmission grid and ADGs. Meanwhile, the diagonal quadratic approximation is adopted to develop an iterative coordination strategy where all local optimization problems are solved in a parallel manner, increasing the computational efficiency. By using the constrained cost variable technique (CCV) and a new affine policy, the original non-convex dispatch model is reformulated as a linear optimization problem, which ensures the convergence of the iterative process and further reduces the computational burden. Case studies on three test systems verify the effectiveness and efficiency of the proposed scheme.