  A new method which allows one to study multiple coherent
reflection/transmissions by partially transparent interfaces, (e.g., in
multi-layer mesoscopic structures or grain boundaries in high-Tc's), in the
framework of the quasiclassical theory of superconductivity is suggested. It is
argued that in the presence of interfaces, a straight-line trajectory
transforms to a simple connected 1-dimensional tree (graph) with knots, i.e.
the points where the interface scattering events occur and pieces of the
trajectories are coupled. For the 2-component trajectory "wave function" which
factorizes the matrix Gor'kov Green's function, a linear boundary condition on
the knot is formulated for an arbitrary interface, specular or diffusive (in
the many channel model). From the new boundary condition, we derive: (i) the
excitation scattering amplitude for the multi-channel Andreev/ordinary
reflection/transmission processes; (ii) the boundary conditions for the Riccati
equation; (iii) the transfer matrix which couples the trajectory Green's
function before and after the interface scattering. To show the usage of the
method, the cases of a film separated from a bulk superconductor by a partially
transparent interface, and a SIS' sandwich with finite thickness layers, are
considered. The electric current response to the vector potential (the
superfluid density $\rho_s$) with the $\pi $ phase difference in S and S' is
calculated for the sandwich. It is shown that the model is very sensitive to
imperfection of the SS' interface: the low temperature response being
paramagnetic ($\rho_s <0$) in the ideal system case, changes its sign and
becomes diamagnetic ($\rho_s > 0$) when the probability of reflection is as low
as a few percent.
