The identification of essential proteins can help in understanding the minimum requirements for cell survival and development. Ever-increasing amounts of high-throughput data provide us with opportunities to detect essential proteins from protein interaction networks (PINs). Existing network-based approaches are limited by the poor quality of the underlying PIN data, which exhibits high rates of false positive and false negative results. To overcome this problem, researchers have focused on the prediction of essential proteins by combining PINs with other biological data, which has led to the emergence of various interactions between proteins. It remains challenging, however, to use aggregated multiplex interactions within a single analysis framework to identify essential proteins. In this study, we created a multiplex biological network (MON) by initially integrating PINs, protein domains, and gene expression profiles. Next, we proposed a new approach to discover essential proteins by extending the random walk with restart algorithm to the tensor, which provides a data model representation of the MON. In contrast to existing approaches, the proposed MON approach considers for the importance of nodes and the different types of interactions between proteins during the iteration. MON was implemented to identify essential proteins within two yeast PINs. Our comprehensive experimental results demonstrated that MON outperformed 11 other state-of-the-art approaches in terms of precision-recall curve, jackknife curve, and other criteria.