We present a novel morphing operator for spatially-varying bidirectional reflectance distribution functions. Our operator takes as input digital materials modeled using a set of 2D texture maps which control the typical parameters of a standard BRDF model. It also takes an interpolation map, defined over the same texture domain, which modulates the interpolation at each texel of the material. Our algorithm is based on a transport mechanism which continuously transforms the individual source maps into their destination counterparts in a feature-sensitive manner. The underlying non-rigid deformation is computed using an energy minimization over a transport grid and accounts for the user-selected dominant features present in the input materials. During this process, we carefully preserve details by mixing the material channels using a histogram-aware color blending combined with a normal reorientation. As a result, our method allows to explore large regions of the space of possible materials using exemplars as anchors and our interpolation scheme as a navigation mean. We also give details about our real time implementation, designed to map faithfully to the standard physically-based rendering workflow and letting users rule interactively the morphing process.