We study the occurrence of negative differential conductance induced by resonance effects in a model for a multilayer heterostructure. In particular, we consider a system consisting of several correlated and noncorrelated monatomic layers sandwiched between two metallic leads. The geometry confines electrons in wells within the heterostructures, which are connected to each other and to the leads by tunneling processes. The nonequilibrium situation is produced by applying a bias voltage to the leads. Our results show that, for specific values of the parameters, resonance tunneling takes place. We investigate in detail its influence on the current-voltage characteristics. Our results are obtained via nonequilibrium real-space dynamical mean-field theory. As an impurity solver we use the so-called auxiliary master equation approach, which addresses the impurity problem within an auxiliary system consisting of a correlated impurity, a small number of uncorrelated bath sites, and two Markovian environments described by a generalized master equation.