A system of linear reaction-diffusion equations with nonlinear singular own sources is considered in this paper. Compatibility conditions provided sufficient regularity of the solution are derived. A second order accurate immersed interface difference scheme is constructed for the differential system of equations involving interfaces. The numerical method is more accurate than the standard approach and does not require the interfaces to be grid points. An algorithm for decoupling of the difference equations in nonlinear part (with small number of equations) and linear part (with large number of equations) is proposed. Numerical experiments are discussed.