Although strong and stiff human-made composites have long been developed, the microstructure of today's most advanced composites has yet to achieve the order and sophisticated hierarchy of hybrid materials built up by living organisms in nature. Clay-based nanocomposites with layered structure can reach notable stiffness and strength, but these properties are usually not accompanied by the ductility and flaw tolerance found in the structures generated by natural hybrid materials. By using principles found in natural composites, we showed that layered hybrid films combining high tensile strength and ductile behavior can be obtained through the bottom-up colloidal assembly of strong submicrometer-thick ceramic platelets within a ductile polymer matrix.