The mechanics of collagen-fibrin co-gels are useful and scientifically interesting. These proteins, along with elastin, are major components of connective tissue in the human body, and understanding how they interact can help shed light on the mechanics of human tissue. Scaffolds made of these networks are a staple of tissue engineering research. However, the relationship between the properties of the pure components and those of the co-gels has been difficult to specify. Our group has previously found that at high collagen fractions, co-gels behave according to a parallel (solid mixture) model, but fibrin-rich gels exhibit more series-like behavior. This observed phenomenon suggests there is a fundamental change in the way the two components interact as the co-gel’s composition changes. In this study, we explored the hypothesis that this interesting mechanical behavior stems from failure of the dilute component to form a fully percolating network. The hypothesis seemed plausible because a nonpercolating dilute network would only be able to affect the co-gel’s behavior with fiber-fiber interactions, which would resemble a series model. To test this hypothesis, we generated a set of computational model networks in which the high-density component percolates the model space but the low-density component does not, instead occupying a small island embedded within the larger network. When the composite model is stretched, the only stretching the embedded network experiences is due to the crosslinks between the major and minor networks. When we applied this model to collagen-rich co-gels with embedded fibrin islands, the mechanics of the stiffer collagen gel were largely unaffected by the embedded fibrin gel, leading to parallel behavior at the macroscopic scale, consistent with our hypothesis. However, when a stiff collagen network was embedded in the more compliant fibrin network, the fibrin network’s deformation was not markedly altered either. The parallel model exhibited an earlier transition in behavior, but neither model was able to replicate the experimental results. It is likely that the underlying model underestimates how much the proteins interact with each other and that a parallel-like model with much more internetwork fiber interaction would capture the experimentally observed behavior better.