We propose receivers for bistatic sensing and communication that exploit a tensor modeling of the received signals. We consider a hybrid scenario where the sensing link knows the transmitted data to estimate the target parameters while the communication link operates semi-blindly in a direct data decoding approach without channel knowledge. We show that the signals received at the sensing receiver and communication receiver follow PARATUCK and PARAFAC tensor models, respectively. These models are exploited to obtain accurate estimates of the target parameters (at the sensing receiver) and the transmitted symbols and channels (at the user equipment). We discuss uniqueness conditions and provide some simulation results to evaluate the performance of the proposed receivers. Our experiments show that the sensing parameters are well estimated at moderate signal-to-noise ratio (SNR) while keeping good symbol error rate (SER) and channel normalized mean square error (NMSE) results for the communication link.