We studied two-dimensional (2-D) thin dielectric parabolic reflector, sandwiched by thin resistive layer from both sides. It is illuminated by an E-polarized electromagnetic plane wave from front side. It is expected to observe the radiation performance of such a composite reflector depending on the electrical and geometrical parameters. We applied two-sided generalized boundary conditions which are modified for a thin multilayer structure. The electromagnetic boundary value problem is formulated and it finally produced a set of two coupled singular integral equations (SIEs). They are handled with the analytical regularization method based on the Riemann-Hilbert Problem solution. The final numerical results are in the Fredholm second-kind matrix equation form and any desired accuracy can possibly be obtained. Also the solution procedure guarantees the convergence. It is observed that the proper selection of the electrical resistivity of the thin resistive layer produces wider bandwidth in the aperture efficiency and the directivity variation approaches to the perfect electric conductor (PEC) reflector case for higher dielectric constants. This selection can increase the allowable frequency band in the applications by coating dielectric layer from both sides. We demonstrate these statements in the numerical results section in the microwave frequency range.