select the planar surface and in the attribute editor crank up the tesselation od the U and V to about 4 or 5. to this to both obkects. The higher the number the longer the render. So only go as far as you need to. mtmckinley mentioned converting to polys. This may be a wise choice depending on what you are doing next with this.

You can just convert the beveled surface to poly and than select the inner edges and fill hole. Should work.