Revealing underlying relations between nodes in a network is one of the most important tasks in network analysis. Using tools and techniques from a variety of disciplines, many community recovery methods have been developed for different scenarios. Despite the recent interest on community recovery in multilayer networks, theoretical results on the accuracy of the estimates are few and far between. Given a multilayer, e.g. temporal, network and a multilayer stochastic block model, we derive bounds for sufficient separation between intra- and inter-block connectivity parameters to achieve posterior exact and almost exact community recovery. These conditions are comparable to a well known threshold for community detection by a single-layer stochastic block model. A simulation study shows that the derived bounds translate to classification accuracy that improves as the number of observed layers increases.