We consider the community recovery problem on a multilayer variant of the hypergraph stochastic block model (HSBM). Each layer is associated with an independent realization of a d-uniform HSBM on N vertices. Given the similarity matrix containing the aggregated number of hyperedges incident to each pair of vertices, the goal is to obtain a partition of the N vertices into disjoint communities. In this work, we investigate a semidefinite programming (SDP) approach and obtain information-theoretic conditions on the model parameters that guarantee exact recovery both in the assortative and the disassortative cases.