The growing use of composite materials in engineering applications accelerated the de- mand for computational methods, such as multiscale modeling, to accurately predict their behavior. While combining different materials helps achieve optimal structural per- formance, the complex nature of the resulting material behavior poses several challenges. However, multiscale methods based on computational homogenization are hindered by a computational bottleneck, limiting their widespread industrial adoption. A popular approach to address that issue is using surrogate models, which are highly flexible and have been used to successfully predict a wide range of behaviors. However, applications involving microscale damage and fracture remain largely unexplored. This work aims to extend a recent surrogate to include the effect of debonding at the fiber- matrix interface while capturing path-dependent behavior and minimizing the size of the training dataset with excellent extrapolation ability. The proposed model is based on Physically Recurrent Neural Networks [1], where the core idea is to implement the exact material models from the micromodel into the hidden layer of the network. Cohesive integration points with a Cohesive Zone Model are integrated within the network, along with the bulk integration points which in this case correspond to the material models assigned to the fibers and/or matrix. The limitations of the existing architecture are briefly discussed and taken into account for the proposal of novel architectures that better represent the debonding phenomenon and the stress homogenization procedure. In the proposed layout, the history variables of the cohesive points are seen as a set of extra latent features that help determine the local strains of the bulk points. Different architectures are evaluated starting with small training datasets. To maximize 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.