We report a general method for the synthesis of core-shell hybrid materials containing a microporous zeolite core with an aqueous miscible organic-layered double hydroxide (AMO-LDH) shell using a simple in situ coprecipitation method. For example, zeolite-HY@AMO-Mg2Al-CO3-LDH contains a 150 nm hierarchical AMO-Mg2Al-CO3-LDH surface coating on zeolite-HY. It exhibits a similar BET surface area (698 m2 g-1) as the parent zeolite-HY but this surface area has been re-allocated between microspores and mesopores. We believe that surface aluminium sites act as nucleation sites for the formation of the LDH coating and so robustly links it into the zeolite lattice. We expect that this new hybrid structure with micropores dominating in the core and mesopores populating the shell will provide a desirable new hybrid structure type for adsorption or catalysis.