Inspired by the structure and functions of the human skin, a highly sensitive capacitive-piezoelectric flexible sensing skin with fingerprint-like patterns to detect and discriminate between spatiotemporal tactile stimuli including static and dynamic pressures and textures is presented. The capacitive-piezoelectric tandem sensing structure is embedded in the phalange of a 3D-printed robotic hand, and a tempotron classifier system is used for tactile exploration. The dynamic tactile sensor, interfaced with an extended gate configuration to a common source metal oxide semiconductor field effect transistor (MOSFET), exhibits a sensitivity of 2.28kPa(-1). The capacitive sensing structure has nonlinear characteristics with sensitivity varying from 0.25kPa(-1) in the low-pressure range (<100Pa) to 0.002kPa(-1) in high pressure (<approximate to>2.5kPa). The output from the presented sensor under a closed-loop tactile scan, carried out with an industrial robotic arm, is used as latency-coded spike trains in a spiking neural network (SNN) tempotron classifier system. With the capability of performing a real-time binary naturalistic texture classification with a maximum accuracy of 99.45%, the presented bioinspired skin finds applications in robotics, prosthesis, wearable sensors, and medical devices.