  We study the fluctuations of the interface, in the steady state, of the
Surface Relaxation Model (SRM) in two scale free interacting networks where a
fraction $q$ of nodes in both networks interact one to one through external
connections. We find that as $q$ increases the fluctuations on both networks
decrease and thus the synchronization reaches an improvement of nearly $40\%$
when $q=1$. The decrease of the fluctuations on both networks is due mainly to
the diffusion through external connections which allows to reducing the load in
nodes by sending their excess mostly to low-degree nodes, which we report have
the lowest heights. This effect enhances the matching of the heights of low-and
high-degree nodes as $q$ increases reducing the fluctuations. This effect is
almost independent of the degree distribution of the networks which means that
the interconnection governs the behavior of the process over its topology.
