The model of Cruzeiro-Hansson et al. (Biochim. Biophys. Acta (1989) 979, 166-1176) for lipid-cholesterol bilayers at low cholesterol concentrations is used to predict the thermodynamic properties and the passive ion permeability of lipid bilayers as a function of acyl-chain length and cholesterol concentration. Numerical simulations based on the Monte Carlo method are used to determine the equilibrium state of the system near the main gel-fluid phase transition. The permeability is calculated using an ansatz which relates the passive permeability to the amount of interfaces formed in the bilayer when cholesterol is present. The model predicts at low cholesterol contents an increase in the membrane permeability in the transition region both for increasing cholesterol concentration and for decreasing chain length at a given value of the reduced temperature. This is in contrast to the case of lipid bilayers containing high cholesterol concentrations where the cholesterol strongly surpresses the permeability. Experimental results for the Na⁺ permeability of C₁₅PC and DPPC (C₁₆PC) bilayers containing cholesterol are presented which confirm the theoretical predictions at low cholesterol concentrations.