This paper proposes a teleimpedance controller with tactile feedback for more intuitive control of the Pisa/IIT SoftHand. With the aim to realize a robust, efficient and low-cost hand prosthesis design, the SoftHand is developed based on the motor control principle of synergies, through which the immense complexity of the hand is simplified into distinct motor patterns. Due to the built-in flexibility of the hand joints, as the SoftHand grasps, it follows a synergistic path while allowing grasping of objects of various shapes using only a single motor. The DC motor of the hand incorporates a novel teleimpedance control in which the user's postural and stiffness synergy references are tracked in real-time. In addition, for intuitive control of the hand, two tactile interfaces are developed. The first interface (mechanotactile) exploits a disturbance observer which estimates the interaction forces in contact with the grasped object. Estimated interaction forces are then converted and applied to the upper arm of the user via a custom made pressure cuff. The second interface employs vibrotactile feedback based on surface irregularities and acceleration signals and is used to provide the user with information about the surface properties of the object as well as detection of object slippage while grasping. Grasp robustness and intuitiveness of hand control were evaluated in two sets of experiments. Results suggest that incorporating the aforementioned haptic feedback strategies, together with user-driven compliance of the hand, facilitate execution of safe and stable grasps, while suggesting that a low-cost, robust hand employing hardware-based synergies might be a good alternative to traditional myoelectric prostheses.