<p>In many real-world systems, the spatial diffusion process occurs not in the continuous medium but in the discrete, networked substrate, where the multiple interaction layers may coexist. This work introduces a hybrid framework that combines the reaction-diffusion dynamics with cross-network electrical coupling in the FitzHugh-Nagumo (FHN) system on homogeneous and heterogeneous networks. The conditions for Turing instability are derived: for the unidirectionally coupled FHN system on heterogeneous networks and for the bidirectionally coupled FHN system on homogeneous networks. Furthermore, the Turing bifurcation is analysed when the coupling strength serves as the bifurcation parameter. Next, the bidirectionally coupled FHN system on heterogeneous networks is simplified based the slow-fast framework with the pronounced differences between the diffusion rates. The local stability at the stationary state and the necessary parameter bounds for Turing instability are investigated. Numerical simulations on Erdős-Rényi networks validate the analytical thresholds and illustrate the transition from stability to pattern formation. These results open new avenues for understanding how multi-layer network structure and cross-network coupling cooperate to generate the self-organized patterns in the excitable medium.</p>