Flow experiments involving cocurrent and countercurrent spontaneous water/oil imbibition were performed on the same laterally coated sample of a natural porous medium with local saturation measurements and various boundary conditions. The experiments with countercurrent imbibition showed slower oil recovery, a smoother water/oil front, and slightly lower ultimate oil recovery than those with predominantly cocurrent imbibition. Numerical simulations revealed that the relative permeabilities that enabled good prediction of countercurrent oil recovery rate are about 30% less than the conventional cocurrent relative permeabilities at a given water saturation. Viscous coupling is assumed to be the origin of this difference. A new formulation of Darcy equations that uses a matrix of mobilities was found to be in qualitative agreement with experimental results.