A porous material is the combination of a solid phase and a fluid phase, with interactions and energy exchanges between phases giving rise to the dissipation of waves traveling through the porous medium. In air, mostly viscous effects and thermal effects are responsible for dissipation, in a way that strongly depends on the pore microstructure. To evaluate the intrinsic properties pertaining to this microstructure, inverse acoustic methods have been used in the past, typically using impedance tubes to observe the way a porous sample interacts with an acoustic field. The impedance tube is a widespread tool in the acoustic community and has proven to be efficient in retrieving, via an inverse method, porous material intrinsic properties such as the porosity or the tortuosity of a sample. In this work, a Bayesian representation of knowledge is taken, where information on a material property is encoded in a probability density function. When multi-layer materials are considered, classical inverse methods become ill-posed and it might become impossible to retrieve exactly each layers intrinsic properties. This work presents two straightforward improvements that can be used in order to lift this ill-posedness and increase the precision with which material properties are obtained.