This work deals with a nonlinear mass transfer problem in an infinite combined domain, consisting of half-space matched to a bounded part via a thin intermediate layer. The latter exhibits high contrast material properties, whereas its thickness is assumed to be negligible in comparison with the dimensions of the bounded subdomain. The corresponding problem is reduced to an auxiliary one, defined only in the bounded region with a non-local boundary condition on the transmission surface, which is solved numerically by means of FEM. To introduce the boundary condition, a special iterative subroutine based on the classic Robin type boundary condition is constructed. The accuracy of the procedure and the range of its applicability are investigated for an analytical benchmark. Numerical results for an axisymmetrical stationary mass transfer problem are presented.