This paper explores the novel approach to solve the synchronisation challenges in stochastic multi-layer networks (SMLNs). Initially, the paper introduces a novel strategy termed event-triggered delayed impulsive control (ETDIC) to account for time delay effects in control. Here, the impulsive moment is determined by a pre-designed event-triggered mechanism (ETM). Additionally, by integrating the Lipschitz-Razumikhin method with graph theory, the study establishes a minimal positive lower bound on the event separation time. This bound effectively prevents Zeno behavior and establishes adequate conditions for ensuring synchronization in SMLNs. Finally, the theoretical results are verified by numerical example.