To cope with the impact of predicted source-load deviations on the optimal dispatch of ac/dc hybrid microgrids at different time scales, this paper develops a multiple-time-scale (MTS) rolling optimal dispatching framework. A novel day-ahead distributionally robust optimization (DRO) model, based on the predicted means, deviations, and confidence probabilities of the source-load power, reduces the conservativeness of the adaptive robust optimization and provides robust day-ahead scheduling plans. The source-load deviations are effectively compensated by an MTS rolling optimization for the intraday dispatch, which adjusts the operating power of the controllable units. Relaxed penalty cost functions and rigid constraints on the state of charge are added to ensure cyclic regulation of the energy storage. The superiority and validity of the day-ahead DRO model and the intraday MTS rolling optimization model are verified in case studies.