Risk assessment of storage requires the use of geophysical monitoring techniques to quantify changes in selected reservoir properties such as saturation, pore pressure, and porosity. Conformance monitoring and the associated decision making rest upon the quantified properties derived from geophysical data, with uncertainty assessment. We have developed a general framework combining seismic and controlled-source electromagnetic (CSEM) inversions with rock-physics inversion with fully Bayesian formulations for proper quantification of uncertainty. The Bayesian rock-physics inversion rests upon two stages. First, a search stage consists of exploring the model space and deriving models with the associated probability density function (PDF). Second, an appraisal or importance sampling stage is used as a “correction” step to ensure that the full model space is explored and that the estimated posterior PDF can be used to derive quantities such as marginal probability densities. Both steps are based on the neighborhood algorithm. The approach does not require any linearization of the rock-physics model or assumption about the model parameters’ distribution. After describing the storage context, the available data at the Sleipner field before and after injection (baseline and monitor), and the rock-physics models, we perform an extended sensitivity study. We find that prior information is crucial, especially in the monitor case. We determine that joint inversion of seismic and CSEM data is also key to properly quantifying saturations. Finally, we apply the full inversion strategy to real data from Sleipner. We obtain rock frame moduli, porosity, saturation, and patchiness exponent distributions and the associated uncertainties along a 1D profile before and after injection. The results are consistent with geology knowledge and reservoir simulations, i.e., that the saturations are larger under the caprock confirming the upward migration by buoyancy effect. The estimates of the patchiness exponent have a larger uncertainty, suggesting semipatchy mixing behavior.