Based on the principles of statistical thermodynamics the thermodynamic inconsistency of the Flory-Huggins theory resulting from the random mixing approximation and several serious logical gaps present in the Guggenheim quasi-chemical approximation are demonstrated. We present a unified recursive lattice theory of a general multicomponent polymer mixture. The resulting theory is obtained by solving the lattice model on the simplest recursive lattice known as a Bethe lattice. We also compare our theory with the Flory-Huggins theory and the Guggenheim random-mixing and quasi-chemical approaches. We have proved that the quasi-chemical approximation can be derived directly from the Bethe lattice calculations for a general multicomponent polymer mixture. Our theory reduces to the Flory-Huggins theory in the special limit to be called the random mixing approximation limit and to the Guggenheim quasi-chemical approximation theory is a definite improvement over the Flory-Huggins and the quasi-chemical approaches.