Quantitative estimation of reservoir parameters from seismic observations is a primary objective of reservoir characterization. Accurate prediction of reservoir elastic and petrophysical parameters is of great significance for reservoir evaluation, sweet-spot identification, and subsequent development deployment. However, conventional stepwise seismic inversion methods are prone to error accumulation during the propagation from elastic-parameter inversion to petrophysical-parameters prediction. Although various simultaneous inversion methods have been proposed, deep learning-based approaches that simultaneously estimate elastic and petrophysical properties while incorporating rock physics constraints and seismic forward consistency remain relatively limited. We propose an intelligent multi-parameter joint inversion method (MPJ-Inv) for seismic reservoirs to jointly predict P-wave velocity, S-wave velocity, density, porosity, gas saturation, and shale volume. Specifically, a rock-physics model that accounts for stiff and soft pores was introduced, and a forward operator from petrophysical parameters to seismic data was constructed by combining this model with a linearized approximation of the Zoeppritz equation. In terms of network architecture, an end-to-end joint inversion network composed of an elastic-parameters prediction module and a petrophysical-parameters prediction module was developed. After the elastic-parameters prediction module obtained the elastic parameters, they were used as guiding information and combined with the initial petrophysical model to simultaneously predict petrophysical parameters. During network training, a semi-supervised strategy was adopted. At well locations, well-log labels were used to monitor both elastic and petrophysical parameters; at non-well locations, synthetic seismic data were generated using the forward operator and compared with the observed seismic records. In addition, a rock-physics consistency constraint was introduced to ensure agreement between the elastic and petrophysical parameters predicted by the network, thereby reducing the ill-posedness of the inversion to some extent. Tests on a synthetic seismic dataset and a tight sandstone gas reservoir dataset from Southwest China showed that, compared with conventional sequential inversion, the proposed method achieved higher accuracy, providing an effective reference for joint prediction of sandstone reservoirs.