We study the effects of phase separation on the growth of thin solid f
ilms by molecular beam epitaxy. We propose a continuum theory that tak
es into account the fluctuations of the free surface and the phase sep
aration and explain how bulk lamellar patterns develop from a competit
ion between the surface phase separation and the constant burial of su
rface domains by the incoming beam. The dependence of the wavelength o
n the deposition rate is in excellent agreement with previous Monte Ca
rlo results. We demonstrated that the free surface is modulated, with
a period that is half the bulk modulation wavelength.