  Existence, stability and dynamics of soliton complexes, centered at the site
of a single transverse link connecting two parallel 2D (two-dimensional)
lattices, are investigated. The system with the on-site cubic self-focusing
nonlinearity is modeled by the pair of discrete nonlinear Schr\"{o}dinger
equations linearly coupled at the single site. Symmetric, antisymmetric and
asymmetric complexes are constructed by means of the variational approximation
(VA) and numerical methods. The VA demonstrates that the antisymmetric soliton
complexes exist in the entire parameter space, while the symmetric and
asymmetric modes can be found below a critical value of the coupling parameter.
Numerical results confirm these predictions. The symmetric complexes are
destabilized via a supercritical symmetry-breaking pitchfork bifurcation, which
gives rise to stable asymmetric modes. The antisymmetric complexes are subject
to oscillatory and exponentially instabilities in narrow parametric regions. In
bistability areas, stable antisymmetric solitons coexist with either symmetric
or asymmetric ones.
