Soft robots offer significant advantages in adaptability, safety, and dexterity compared to conventional rigidbody robots. However, it is challenging to equip soft robots with accurate proprioception and exteroception due to their high flexibility and elasticity. In this work, we develop a novel exoskeleton-covered soft finger with embedded cameras and deep learning methods that enable high-resolution proprioceptive sensing and rich tactile sensing. To do so, we design features along the axial direction of the finger, which enable highresolution proprioceptive sensing, and incorporate a reflective ink coating on the surface of the finger to enable rich tactile sensing. We design a highly underactuated exoskeleton with a tendon-driven mechanism to actuate the finger. Finally, we assemble 2 of the fingers together to form a robotic gripper and successfully perform a bar stock classification task, which requires both shape and tactile information. We train neural networks for proprioception and shape (box versus cylinder) classification using data from the embedded sensors. The proprioception CNN had over 99% accuracy on our testing set (all six joint angles were within 1 • of error) and had an average accumulative distance error of 0.77 mm during live testing, which is better than human finger proprioception. These proposed techniques offer soft robots the high-level ability to simultaneously perceive their proprioceptive state and peripheral environment, providing potential solutions for soft robots to solve everyday manipulation tasks. We believe the methods developed in this work can be widely applied to different designs and applications.