Operating on electricity markets requires accurately identifying, quantifying, and measuring risk coupled with their corresponding return: this appears as a crucial point, particularly during and after the COVID-19 pandemic. The aim of the present paper is twofold. First, we propose a novel econometric approach to identifying relevant market factors that capture several elements of the risk transmission mechanism inherent in energy systems. The proposed model extends Bayesian graphical models with change points to a multiple-layer set-up. Multilayer graphs encompass the two relevant channels of shock transmission: volatility and price contagion effects. The choice of these two layers seems natural because electricity prices and their spiky nature, coupled with inherent volatility, constitute essential influential elements for market players to maximize their profits. The change-point specification allows for detecting relevant changes in the electricity market. Second, we apply the proposed econometric framework to the Italian zonal markets analyzing the effects of returns and volatility contagion in several periods detected by the model. The last time intervals identified by the change-point methodology overlap the COVID-19 pandemic period. The model captures relevant abrupt changes in prices and volatility in the zonal electricity market and provides new evidence of interconnections in the zones of the Italian market related to the risk alone, price process alone, and risk versus price process relationship and their interactions.