A new lattice theory is proposed to describe nonrandom mixing behavior based on recently developed lattice model theory by Aranovich and Donohue. The present theory assumes multi-references in order to take into account interference effects on non-random mixing among pairs. The number of references was obtained from Monte Carlo simulations for monomer+hole mixtures. Monte Carlo simulation for hole [0]+monomer [1]+monomer [2] mixture shows that this theory is more accurate than Guggenheim’s quasi-chemical theory or the Aranovich-Donohue model in a wide range of temperatures and densities. Especially, even under the stringent condition of zero interaction energy parameter ε_12=0, the present theory predicts well the extent of nonrandom mixing. For dimer fluid the non-randomness is calculated using the surface fraction. Here three references was used as in the case of monomer fluid with chain connectivity constraints. Comparison of the theory with Monte Carlo simulation results for dimer+hole system shows a good agreement.