In this work, we extend a recent surrogate modeling approach, the Physically Recurrent Neural Network (PRNN), to include the effect of debonding at the fiber–matrix interface of composite materials. The core idea of the PRNN is to implement the exact material models from the micromodel into one of the layers of the network to capture path-dependent behavior implicitly. For the case of debonding, additional material points with a cohesive zone model are integrated within the network, along with the bulk points associated to the fibers and/or matrix. The limitations of the existing architecture are discussed and taken into account for the development of novel architectures that better represent the stress homogenization procedure. In the proposed layout, the history variables of cohesive points act as extra latent features that help determine the local strains of bulk points. Different architectures are evaluated starting with small training datasets. To maximize the predictive accuracy and extrapolation capabilities of the network, various configurations of bulk and cohesive points are explored, along with different training dataset types and sizes.