Multiplex networks provide a fundamental framework for describing complex systems in which the same set of nodes interact through multiple types of connections. Inferring the layer-specific topology of such networks is essential for understanding their structural organization and dynamical behavior. Most existing reconstruction methods, however, rely on the assumption that node states in each layer can be observed separately. This assumption is often diffcult to satisfy in privacy-sensitive, resource-limited, or experimentally constrained scenarios, where only cross-layer aggregated node states are available. In this work, we study the reconstruction of multiplex networks from aggregated observations and propose a Bayesian reconstruction framework based on a Gaussian mixture model. Taking evolutionary game dynamics on multiplex networks as a representative example, we first transform the aggregated payoff observations into a linear inverse problem, in which the unknown variables encode the adjacency information of all layers. To improve the reliability of reconstruction under limited and noisy observations, we introduce a layer-wise Gaussian mixture prior for the edge values. This prior only assumes that each layer contains two possible edge states, without requiring the explicit values of these states. The edge values, mixture weights, variances, interlayer coupling parameters, and observation noise level are then adaptively estimated through an iterative expectation-maximization procedure. Numerical experiments on synthetic multiplex networks driven by evolutionary game dynamics show that the proposed method achieves robust reconstruction performance, especially when the networks are relatively dense or the observations contain strong noise. In these regimes, sparsity-based Lasso reconstruction deteriorates, whereas Signallasso depends on stronger prior knowledge of the edge values. Experiments on real-world multiplex trade networks further demonstrate the applicability of the proposed framework. These results indicate that layer-resolved network structures can be inferred from cross-layer aggregated signals with only weak prior information. The proposed method therefore provides a feasible approach for reconstructing multiplex networks under incomplete observations.