Inspired by the imbricated scale-tissue flexible armor of elasmoid fish, we design hybrid stiff plate/soft matrix material architectures and reveal their ability to provide protection against penetration while preserving flexibility. Indentation and bending tests on bio-inspired 3D-printed prototype materials show that both protection and flexibility are highly tunable by geometrical parameters of the microstructure (plate inclination angle and volume fraction). We show that penetration resistance can be amplified by a factor of 40, while flexibility decreases in less than 5 times. Different deformation resistance mechanisms are found to govern flexibility (inter-plate matrix shear) versus penetration resistance (localized plate bending) for this microstructural architecture which, in turn, enables separation of these functional requirements in the material design. These experiments identify the tradeoffs between these typically conflicting properties as well as the ability to design the most protective material architecture for a required flexibility, providing new design guidelines for enhanced flexible armor systems.