Wettability, or preferential affinity of a fluid to a solid substrate in the presence of another fluid, plays a critical role in the statics and dynamics of fluid-fluid displacement in porous media. The complex confined geometry of porous media, however, makes upscaling of microscopic wettability to the macroscale a nontrivial task. Here, we elucidate the contribution of pore geometry in controlling the apparent wettability characteristics of a porous medium. Using direct numerical simulations of fluid-fluid displacement, we study the reversal of interface curvature in a single converging-diverging capillary, and demonstrate the co-existence of concave and convex interfaces in a porous medium—a phenomenon that we also observe in laboratory micromodel experiments. We show that under intermediate contact angles the sign of interface curvature is strongly influenced by the pore geometry. We capture the interplay between surface chemical properties and pore geometry in the form of a dimensionless quantity, the apparent wettability number, which predicts the conditions under which concave and convex interfaces co-exist. Our findings advance the fundamental understanding of wettability in confined geometries, with implications to macroscopic multiphase-flow processes in porous media, from fuel cells to enhanced oil recovery.