A widely used approach to hyperspectral image classification is to model a mixed-pixel vector as a linear superposition of substances resident in a pixel with additive Gaussian noise. Using this linear mixture model many image processing techniques can be applied, such as linear unmixing or orthogonal subspace projection. However, a third source not considered in this model, called interference (clutter or structured noise), may sometimes give rise to more serious signal deterioration than the additive noise. We address this issue by introducing the interference into the linear mixture model. Including interference in the model enables us to treat the interference as another undesired source, like a passive jammer, so that it can be eliminated prior to detection and classification. This is particularly useful for hyperspectral images, which tend to have a high SNR but a low signal-to-interference ratio with the interference difficult to identify. To find and reject interference, we propose an unsupervised vector quantization-based interference rejection (UIR) approach in conjunction with either an orthogonal subspace projection (OSP) or an oblique subspace projection (OBSP) to simultaneously project a pixel into signature space as well as to null out interference. Since there is no prior knowledge about the interference, the UIR is implemented in an unsupervised manner to generate the desired interference clusters so that they can be annihilated by the OSP or OBSP. The proposed approach is shown by evaluation with Hyperspectral Digital Imagery Collection Experiment (HYDICE) data to exhibit considerable improvement in comparison to linear unmixing or the OSP where interference is not considered.