Proprioception, a key sensory modality in haptic perception, plays a vital role in perceiving the 3D structure of objects by providing feedback on the position and movement of body parts. The restoration of proprioceptive sensation is crucial for enabling in-hand manipulation and natural control in the prosthetic hand. Despite its importance, proprioceptive sensation is relatively unexplored in an artificial system. In this work, we introduce a novel platform that integrates a soft anthropomorphic robot hand (QB SoftHand) with flexible proprioceptive sensors and a classifier that utilizes a hybrid spiking neural network with different types of spiking neurons to interpret neuromorphic proprioceptive signals encoded by a biological muscle spindle model. The encoding scheme and the classifier are implemented and tested on the datasets we collected in the active exploration of ten objects from the YCB benchmark. Our results indicate that the classifier achieves more accurate inferences than existing learning approaches, especially in the early stage of the exploration. This system holds the potential for development in the areas of haptic feedback and neural prosthetics.