In this paper, we introduce a new class of stochastic multilayer networks. A stochastic multilayer network is the aggregation of M networks (one per layer) where each is a subgraph of a foundational network G. Each layer network is the result of probabilistically removing links and nodes from G. e resulting network includes any link that appears in at least K layers. is model is an instance of a non-standard site-bond percolation model. Two sets of results are obtained: rst, we derive the probability distribution that the M-layer network is in a given connguration for some particular graph structures (explicit results are provided for a line, an algorithm is provided for a tree), where a connguration is the collective state of all links (each either active or inactive). Next, we show that for appropriate scalings of the node and link selection processes in a layer, links are asymptotically independent as the number of layers goes to innnity, and follow a Poisson distribution. Numerical results are provided to highlight the impact of having several layers on some metrics of interest (including expected size of the cluster a node belongs to in the case of the line). is model nds applications in wireless communication networks with multichannel radios, multiple social networks with overlapping memberships, transportation networks, and, more generally, in any scenario where a common set of nodes can be linked via co-existing means of connectivity.