The distribution function between diffusion and spin relaxation time is shown to be a powerful tool to characterize fluid mixtures in porous media. We discuss the nuclear magnetic resonance measurements using diffusion-editing sequences that were developed to measure this quantity. A recently developed two-dimensional inversion routine is used to extract the distribution function from the data. We show both theoretically and experimentally that the technique is suitable for ex situ applications in the presence of grossly inhomogeneous fields. We apply this technique to characterize sedimentary rocks saturated with oil-water mixtures. From the measured diffusion-relaxation time distribution function it is possible to quantify the oil and water saturation, to get a direct indication of the wettability of the porous media, to characterize the bulk properties of the oil and estimate the oil viscosity, and to get information about the geometrical arrangement of the fluid phases in the pore space. We have also identified effects due to susceptibility induced gradients in a sandstone and effects of strongly restricted diffusion in a limestone.