In the last decade, the main attacks against smart grids have occurred in communication networks (ITs) causing the disconnection of physical equipment from power networks (OTs) and leading to electricity supply interruptions. To deal with the deficiencies presented in past studies, this paper addresses smart grids vulnerability assessment considering the smart grid as a cyber-physical heterogeneous interconnected system. The model of the cyber-physical system is composed of a physical power network model and the information and communication technology network model (ICT) both are interconnected and are interrelated by means of the communication and control equipment installed in the smart grid. This model highlights the hidden interdependencies between power and ICT networks and contains the interaction between both systems. To mimic the real nature of smart grids, the interconnected heterogeneous model is based on multilayer complex network theory and scale-free graph, where there is a one-to-many relationship between cyber and physical assets. Multilayer complex network theory centrality indexes are used to determine the interconnected heterogeneous system set of nodes criticality. The proposed methodology, which includes measurement, communication, and control equipment, has been tested on a standardized power network that is interconnected to the ICT network. Results demonstrate the model’s effectiveness in detecting vulnerabilities in the interdependent cyber-physical system compared to traditional vulnerability assessments applied to power networks (OT).