Recent research has delved into advanced designs for reconfigurable intelligent surfaces (RIS) with integrated sensing functions. One promising concept is the hybrid RIS (HRIS), which blends sensing and reflecting meta-atoms. This enables HRIS to process signals, aiding in channel estimation (CE) and symbol detection tasks. This paper formulates novel semi-blind receivers for HRIS-aided wireless communications that enable joint symbol and CE at the HRIS and BS. The proposed receivers exploit a tensor coding at the transmit side, while capitalizing on the multilinear structures of the received signals. We develop iterative and closed-form receiver algorithms for joint estimation of the uplink channels and symbols at both the HRIS and the BS, enabling joint channel and symbol estimation functionalities. The proposed receivers offer symbol decoding capabilities to the HRIS and ensure ambiguity-free separate CE without requiring an a priori training stage. We also study identifiability conditions that provide a unique joint channel and symbol recovery, and discuss the computational complexities and tradeoffs involved in the proposed semi-blind receivers. Our findings demonstrate the competitive performances of the proposed solutions at the HRIS and the BS and unveil distinct performance trends based on the possible combinations of HRIS-BS receiver pairs. Finally, extensive numerical results elucidate the interplay between power splitting, symbol recovery, and CE accuracy in HRIS-assisted communications. Such insights are pivotal for optimizing receiver design and enhancing system performance in future HRIS deployments.