The thermal stability of a hybrid composite rod, made of epoxy-anhydride matrix reinforced with both unidirectional carbon and glass fibers, has been evaluated between 180 and 210 °C in different nitrogen/oxygen gas mixtures with several conventional but complementary laboratory techniques such as Fourier transform infrared spectrometry, thermogravimetry, differential calorimetry, optical microscopy, and three-point bending. Thermolysis predominates in the carbon-fiber core, where it induces an efficient chain scission process, leading to a decrease in the glass transition temperature and the formation of small macromolecular fragments, presumably diacids. These very polar fragments remain trapped in the carbon core, where they initiate micro-cavities when their concentration exceeds the solubility threshold. These micro-cavities accumulate in rich-matrix regions, where they coalesce to form apparent large cracks. They are thus responsible for the catastrophic decrease in elastic and fracture properties of the composite rod. In contrast, thermal oxidation affects a too thin superficial layer (typically 60 µm) of the glass-fiber shell to change significantly the global mechanical behavior of the composite rod. Based on these experimental observations, a kinetic model has been proposed to predict the initiation and development of damage in the composite rod. Its validity is successfully checked by comparing its predictions with the experimental results.