We present a unified lattice theory for a binary solution where endgroups are treated differently from middle groups. This is a simple example of a triblock and the present study provides a starting point for studying a general triblock system. We replace the original homogeneous lattice by a Bethe lattice of the same coordination number as the original lattice. The model is solved exactly on the Bethe lattice. The resulting solution goes beyond the random mixing approximation and provides us with an approximate theory of the model on the regular lattice. The contributions of endgroups on various thermodynamic properties of a binary solution are investigated in a quantitative way using the theory. In particular, our theory predicts that contributions to the energy are more important than to the entropy.