Physical Human-Robot Interaction (pHRI) is essential for robots that establish contact with humans, like assistive or rescue robots. pHRI demands hard safety and compliance constraints. Tactile sensing is vital for pHRI, as vision and/or range sensors alone can not cope with constant occlusions while grasping. Measuring pressure on the grasping surface is crucial to avoid injury, predict user intent and successfully perform collaborative movements. This work presents a new three-fingered gripper equipped with novel tactile sense capability via arrays of finger pressure sensors. Experiments gripping a human arm on the distal and proximal surfaces of the gripper fingers have been performed to assess sensing performance in the normal and tangential components. Results prove that a good estimation of interaction between human and robot is achieved in both normal and tangential movements.