Application of the belief propagation (BP) algorithm is proposed for pilot-assisted reception of Gaussian distributed symbols over unknown inter-symbol interference channels whose parameters are also Gaussian distributed. The proposed Bayesian network graph for the demodulator includes the channel parameters as explicit nodes, allowing the combined estimation of the channel and information bearing symbols with the aid of pilot symbols. Since direct application of BP is not tractable for this model, the algorithm is obtained by introducing approximations of the message distributions appropriately. The proposed algorithm is parallel in nature, is suitable for sparse channels, and can be easily extended to coded systems for joint demodulation and decoding. The numerical results show near-optimal performance in the minimum mean squared error sense for a small example, and a performance better than that of iterative semi-blind equalization with batch matrix-based estimators for the general case.