  This article continues the research initiated in [17]. We derive explicit
formulae for the leading order profiles of eleven types of stationary solutions
to a one-dimensional two-layer thin-film liquid model considered with an
intermolecular potential depending on both layer heights. The found solutions
are composed of the repeated elementary blocks (bulk, contact line and
ultra-thin film ones) being consistently asymptotically matched together. We
show that once considered on a finite interval with Neumann boundary conditions
these stationary solutions are either dynamically stable or weakly
translationally unstable. Other composite solutions are found to be numerically
unstable and rather exhibit complex coarsening dynamics.
