Fiber reinforced composites are layered materials consisting of several material interfaces. For accurate prediction of their dynamic fracture, it is important to understand the capabilities and limitations of continuum damage models with regards to the behavior of dynamic cracks at interfaces. Accordingly, the goal of this work is to analyze the interactions between a dynamically propagating crack and a material interface and compare the predictions with experiments. For this purpose, benchmark experimental results on a PMMA bi-layer system glued together are considered. The geometry consists of a notched specimen being impacted at the notch root by an impactor in a direction normal to the interface. The model is built in commercial FEA software Abaqus, and the material failure (of both PMMA and the glue) is modeled using an isotropic, strain rate dependent continuum damage model, implemented within the framework of the crack band theory. Modeling shows that similar to experiments, the dynamic crack approaches the interface at a right angle, under pure mode I. It then either penetrates the interface or grows within the interface eventually branching out under mixed mode. This behavior is found to depend on the distance the crack travelled before reaching the interface. It is found that in order to obtain this agreement with experiments, the fracturing rate effects must be included for both the PMMA and the glue, where the strength and fracture energy both depend on the strain rate. Secondly, it is found that an isotropic damage model driven by an effective strain that distinguishes between tension and compression damage is necessary to capture the mixed mode behavior properly. Various definitions of the equivalent strain are evaluated and found to work with varying degrees of success. The sensitivity of this behavior to various material parameters is analyzed too.