Multilayer systems are widely used in industry for their performances as compared with homogeneous materials. The layers are usually glued together but the bonding may be imperfect (air bubble, detachment). The interfaces are generally modeled as sliding or bonded. These two behaviors can be significantly different and the actual behavior is generally somewhere in between. The vibroacoustic behavior of the structure is thus modified by the imperfect interface. Several models have been implemented to describe the dynamic behavior of multilayer systems with imperfect interfaces. In this paper, an analytical model of imperfect interfaces based on the Transfer Matrix Method (TMM) is developed. Two computations are performed in parallel (one with a perfectly bonded interface and the other with a sliding interface). Then, the global transfer matrix obtained from each computation are mixed together. The main novelty of this paper lies in the use of a new mixing method which is applied on the state variables as compared with existing methods which are applied on impedances or admittances matrices. This new method is compared in terms of sound absorption or sound transmission loss with the existing ones and is applied on different classical multilayer systems with multi-layered solid plates and a multilayer composed of a porous layer with a heavy layer which is widely used in the automotive industry.