A method is described for subsurface hydrocarbon reservoir characterization including receiving a time-lapse electromagnetic (EM) dataset and a flow dataset; inverting the time-lapse EM dataset using a parametric inversion that models steel well casings to determine a volume of fluid-changed reservoir; inverting the time-lapse EM dataset and the flow dataset using a joint inversion that honors the volume of the fluid-changed reservoir to determine relative permeability and capillary pressure; and characterizing flow characteristics in the volume of the fluid-changed reservoir. The method may be executed by a computer system.