A new, simple and fast method is presented for determining the location and the shape of a one-dimensional rough interface between two lossy dielectric half-spaces. The reconstruction is obtained from a set of reflected field measurements for a single illumination by a plane wave at a fixed frequency. Through a special representation of the scattered field in the half-spaces above and below the interface in terms of a Fourier transform and a Taylor expansion the problem is first reduced to the solution of a system of two nonlinear operator equations. Then this system is solved iteratively by alternating between a linear equation for a spectral coefficient of the scattered wave and a linearization of a nonlinear equation for the surface profile. The numerical simulations show that the method yields satisfactory reconstructions for slightly rough surface profiles.