In this paper, a class of Gaussian broadcast interference channels is investigated, where one of the two broadcast users is subject to the interference coming from a point-to-point transmission. Channel parameters are categorized into three regimes. For the first two, where an ordering of the decodability of the broadcast users exists, inner bounds based on superposition and rate splitting are obtained. Entropy-power-inequality-based outer bounds are derived by combining bounding techniques for Gaussian broadcast and interference channels. These inner and outer bounds lead to either exact or approximate characterizations of the capacity region and sum capacity under various conditions. For the remaining complementing regime, inner and outer bounds are also provided.