The natural interaction between the prosthetic hand and the upper limb amputation patient is important and directly affects the rehabilitation effect and operation ability. Most previous studies only focused on the interaction of gestures but ignored the force levels. This paper proposes a simultaneous recognition method of gestures and forces for interaction with a prosthetic hand. The multitask classification algorithm based on a convolutional neural network (CNN) is designed to improve recognition efficiency and ensure recognition accuracy. The offline experimental results show that the algorithm proposed in this study outperforms other methods in both training speed and accuracy. To prove the effectiveness of the proposed method, a myoelectric prosthetic hand integrated with tactile sensors is developed, and surface electromyography (sEMG) datasets of healthy persons and amputees are built. The online experimental results show that the amputee can control the prosthetic hand to continuously make gestures under different force levels, and the effect of hand coordination on the hand perception of amputees is explored. The results show that gesture classification operation tasks with different force levels based on sEMG signals can be accurately recognized and comfortably interact with prosthetic hands in real time. It improves the amputees' operation ability and relieves their muscle fatigue.