A stochastic joint-inversion approach for estimating reservoir-fluid saturations and porosity is proposed. The approach couples seismic amplitude variation with angle (AVA) and marine controlled-source electromagnetic (CSEM) forward models into a Bayesian framework, which allows for integration of complementary information. To obtain minimally subjective prior probabilities required for the Bayesian approach, the principle of minimum relative entropy (MRE) is employed. Instead of single-value estimates provided by deterministic methods, the approach gives a probability distribution for any unknown parameter of interest, such as reservoir-fluid saturations or porosity at various locations. The distribution means, modes, and confidence intervals can be calculated, providing a more complete understanding of the uncertainty in the parameter estimates. The approach is demonstrated using synthetic and field data sets. Results show that joint inversion using seismic and EM data gives better estimates of reservoir parameters than estimates from either geophysical data set used in isolation. Moreover, a more informative prior leads to much narrower predictive intervals of the target parameters, with mean values of the posterior distributions closer to logged values.