We present a variational formulation based on the idea of Nitsche's method to account for thin layers in acoustic problems. Pressure jump model of robin-type condition is used to model the effects of thin acoustic layers. The computational domain is discretized using eXtended Finite Element Method (X-FEM) to represent the discontinuity in the elements and to mitigate the meshing restriction for complex geometry of interfaces. The porous materials with complex-valued propertis are also considered in current work, which introduce an energy dissipation in the system.