In this paper, we study the problem of two linear reaction-diffusion equations at the semi-discrete level in space coupled through a nonlinear condition close to the ones used between ocean and atmosphere in Earth System Models. The steady state of the coupled problem is derived analytically and the well-posedness is discussed: using the inverse function theorem, we show how the existence and uniqueness of the solution around the steady state is related to the well-posedness of the linearized problem. A convergence analysis of Schwarz Waveform Relaxation applied to this coupled problem is then pursued in the Fourier domain. This analysis uses the linearization of the problem around the steady state. It is found that the linearized transmission condition leads to a convergence factor that changes from one iteration to another. Finally the relaxation parameter is optimized using the singular values of a transition matrix and a range for this parameter is given for which the SWR converges.