This paper deals with the electromagnetic wave scatteringfrom multi-layered media, containing random rough interfaces.It presents an extension of a basic asymptotic modelcalled the Kirchhoff-tangent plane approximation (KA) tomulti-layers. In order to be able to derive a simple expressionof the scattered intensity, further approximations mustbe made. Here, we focus on calculating only the coherentcontribution to the total scattered intensity and apply the socalledscalar Kirchhoff approximation that makes it possibleto simplify the mathematical expressions. Last, the randomrough interfaces are assumed to be uncorrelated, so that afully analytical expression of the (coherent) scattered intensityis obtained. Previous work validated this approach; thispaper focuses on analysing the hypothesis of taking only onereflection inside each layer into account.