Eyeglasses play an important role in the perception of identity. Authentic virtual representations of faces can benefit greatly from their inclusion. However, modeling the geometric and appearance interactions of glasses and the face of virtual representations of humans is challenging. Glasses and faces affect each other’s geometry at their contact points, and also induce appearance changes due to light transport. Most existing approaches do not capture these physical interactions since they model eyeglasses and faces independently. Others attempt to resolve interactions as a 2D image synthesis problem and suffer from view and temporal inconsistencies. In this work, we propose a 3D compositional morphable model of eyeglasses that accurately incorporates high-fidelity geometric and photometric interaction effects. To support the large variation in eyeglass topology efficiently, we employ a hybrid representation that combines surface geometry and a volumetric representation. Unlike volumetric approaches, our model naturally retains correspondences across glasses, and hence explicit modification of geometry, such as lens insertion and frame deformation, is greatly simplified. In addition, our model is relightable under point lights and natural illumination, supporting high-fidelity rendering of various frame materials, including translucent plastic and metal within a single morphable model. Importantly, our approach models global light transport effects, such as casting shadows between faces and glasses. Our morphable model for eyeglasses can also be fit to novel glasses via inverse rendering. We compare our approach to state-of-the-art methods and demonstrate significant quality improvements.