Structural composites inspired by nacre have emerged as prime exemplars for guiding materials design of fracture-resistant, rigid hybrid materials. The intricate microstructure of nacre, which combines a hard majority phase with a small fraction of a soft phase, achieves superior mechanical properties compared to its constituents and has generated much interest. However, replicating the hierarchical microstructure of nacre is very challenging, not to mention improving it. In this article, we propose to alter the geometry of the hard building blocks by introducing the concept of topological interlocking. This design principle has previously been shown to provide an inherently brittle material with a remarkable flexural compliance. We now demonstrate that by combining the basic architecture of nacre with topological interlocking of discrete hard building blocks, hybrid materials of a new type can be produced. By adding a soft phase at the interfaces between topologically interlocked blocks in a single-build additive manufacturing process, further improvement of mechanical properties is achieved. The design of these fabricated hybrid structures has been guided by computational work elucidating the effect of various geometries. To our knowledge, this is the first reported study that combines the advantages of nacre-inspired structures with the benefits of topological interlocking.