  Fundamental solitons pinned to the interface between two discrete lattices
coupled at a single site are investigated. Serially and parallel-coupled
identical chains (\textit{System 1} and \textit{System 2}), with the
self-attractive on-site cubic nonlinearity, are considered in one dimension. In
these two systems, which can be readily implemented as arrays of nonlinear
optical waveguides, symmetric, antisymmetric and asymmetric solitons are
investigated by means of the variational approximation (VA) and numerical
methods. The VA demonstrates that the antisymmetric solitons exist in the
entire parameter space, while the symmetric and asymmetric modes can be found
below some critical value of the coupling parameter. Numerical results confirm
these predictions for the symmetric and asymmetric fundamental modes. The
existence region of numerically found antisymmetric solitons is also limited by
a certain value of the coupling parameter. The symmetric solitons are
destabilized via a supercritical symmetry-breaking pitchfork bifurcation, which
gives rise to stable asymmetric solitons, in both systems. The antisymmetric
fundamental solitons, which may be stable or not, do not undergo any
bifurcation. In bistability regions stable antisymmetric solitons coexist with
either symmetric or asymmetric ones.
