The authors deal with equations of the form: \[ \text{div} \left( {1\over\mu} \nabla u\right) + k^2\varepsilon u = 0, \] where \(\mu\) and \(\varepsilon\) are periodic on the thin layer (the periodicity is described by tangent coordinates, and the period has the same order of the layer thickness). The problem, by scaling, is reduced to a problem with fixed domain. A class of approximate boundary conditions for the scattering problem by a penetrable obstacle coated with a thin periodic layer are derived.