This work looks at the asymptotic behaviour of the solution to the Helmholtz equation in a penetrable domain of $\mathbb{R}$ 3 with a thin layer of thickness δ which tends to 0. We use the method of multi-scale expansion to derive and justify an asymptotic expansion of the solution with respect to the thickness δ up to any order. We then provide approximate transmission conditions of order two defined on an interface located inside the thin layer, with accuracy up to O (δ 2 ), which allow one to take into account the influence of the thin layer.