Interference-enhanced wide-field nanoparticle imaging is a highly sensitive technique that has found numerous applications in labeled and label-free subdiffraction-limited pathogen detection. It also provides unique opportunities for nanoparticle classification upon detection. More specifically, the nanoparticle defocus images result in a particle-specific response that can be of great utility for nanoparticle classification, particularly based on type and size. In this work, we combine a model-based supervised learning algorithm with a wide-field common-path interferometric microscopy method to achieve accurate nanoparticle classification. We verify our classification schemes experimentally by blindly detecting gold and polystyrene nanospheres, and then classifying them in terms of type and size.