This paper proposes an interval-partitioned uncertainty (IPU) constrained robust dispatch model for an islanded AC/DC hybrid microgrid considering the uncertainties of the generation-load power and the operating states of the bidirectional converter. The IPU sets accurately describe the spatiotemporal distributions of the generation-load power and reduce the conservativeness of traditional single-interval uncertainty set-based robust optimization. To coordinate the scheduling of the uncontrollable renewable generators under uncertain conditions, the operating states of these generators were set as the first- or third-level optimal variables of the min-max-min robust model, which was linearized by the big-M method. The tri-level robust optimization with a mixed-integer recourse problem was quickly solved by a nested column-and-constraint generation algorithm. The validity and rationality of the proposed robust models, uncertainty sets, and solving method were confirmed in case studies.