Within a second virial theory, we study bulk phase diagrams as well as the free planar isotropic-nematic interface of binary mixtures of nonadditive thin and thick hard rods. For species of the same type, the excluded volume is determined only by the dimensions of the particles, whereas for dissimilar ones it is taken to be larger or smaller than that, giving rise to a nonadditivity that can be positive or negative. We argue that such a nonadditivity can result from modeling of soft interactions as effective hard-core interactions. The nonadditivity enhances or reduces the fractionation at isotropic-nematic (IN) coexistence and may induce or suppress a demixing of the high-density nematic phase into two nematic phases of different compositi...