  Interplay between kinetic roughening and phase ordering is studied in a
growth SOS model with two kinds of particles and Ising-like interaction by
Monte Carlo simulations. We found that, for a sufficiently large coupling,
growth is strongly affected by interaction between species. Surface roughness
increases rapidly with coupling. Scaling exponents for kinetic roughening are
enhanced with respect to homogeneous situation. Phase ordering which leads to
the lamellar structure persisting for a long time is observed. Surface profiles
in strong coupling regime have a saw-tooth form, with the correlation between
the positions of local minima and the domain boundaries.
