An in-line fiber coupler, based on side-polished single-mode fibers covered with an intermediate coupling layer and a planar waveguide, is analyzed by modeling the interaction region as an equivalent multi-layered planar waveguide. The reflectance for the multi-layered structure with and without buffer layer is illustrated as a function of the refractive index and thickness of the overlay waveguides. When the refractive index of the overlay waveguides is greater than that of the fiber core, the conditions for the intermediate coupling layer to increase the power coupling from the fiber to the overlays is also explained. Through the experimental results using a LiNbO$_3$planar waveguide, we show that the theoretical analysis is reasonable and in good agreement with the measured values.