Statistical thermodynamic theory developed recently to study self-assembled fluid monolayer films of short diblock copolymeric surfactants at the oil/water inter-face is applied to spread monolayers comprised of mixtures of amphiphiles that differ only in the flexibility of their chains. Although the oil and water solvents are assumed to be athermal for the two blocks of the amphiphiles, we predict large positive deviations from the ideal foe energy of mixing that result in phase separation for sufficiently long chains. Pressure-composition phase diagrams and representative pressure-area isotherms are predicted for monolayer films over a range of chain lengths. By comparing predicted structural properties to the contributions to the mixing free energy, we explore the physical origins of the demixing, and consider its implications for experimental systems such as cholesterol/lipid mixtures in monolayers and bilayers.