Against a general trend of increasing driver longevity, the injuries suffered by vehicle occupants in Spanish road traffic crashes are analyzed by the level of severity of their bodily injuries (BI). Generalized linear mixed models are applied to model the proportion of non-serious, serious, and fatal victims. The dependence between vehicles involved in the same crash is captured by including random effects. The effect of driver age and vehicle age and their interaction on the proportion of injured victims is analyzed. We find a nonlinear relationship between driver age and BI severity, with young and older drivers constituting the riskiest groups. In contrast, the expected severity of the crash increases linearly up to a vehicle age of 18 and remains constant thereafter at the highest level of BI severity. No interaction between the two variables is found. These results are especially relevant for countries such as Spain with increasing driver longevity and an aging car fleet.