  We present a low energy Hamiltonian generalized to describe how the energy
bands of germanene ($\rm \overline{Ge}$) are modified by interaction with a
substrate or a capping layer. The parameters that enter the Hamiltonian are
determined from first-principles relativistic calculations for $\rm
\overline{Ge}|$MoS$_2$ bilayers and MoS$_2|\rm \overline{Ge} |$MoS$_2$
trilayers and are used to determine the topological nature of the system. For
the lowest energy, buckled germanene structure, the gap depends strongly on how
germanene is oriented with respect to the MoS$_2$ layer(s). Topologically
non-trivial gaps for bilayers and trilayers can be almost as large as for a
free-standing germanene layer.
