The physical properties of ultrathin NaCl overlayers on the stepped Cu(311) surface have been characterized using scanning tunneling microscopy (STM) and spectroscopy, and density-functional calculations. Simulations of STM images and differential conductance spectra were based on the Tersoff-Hamann approximation for tunneling with corrections for the modified tunneling barrier at larger voltages and calculated Kohn-Sham states. Characteristic features observed in the STM images can be directly related to calculated electronic and geometric properties of the overlayers. The measured apparent barrier heights for the mono-, bi-, and trilayers of NaCl and the corresponding adsorption-induced changes in the work function, as obtained from the distance dependence of the tunneling current, are well reproduced and explained by the calculated results. The measurements revealed a large reduction of the tunneling conductance in a large voltage range, resembling a band gap. However, the simulated spectrum showed that only the onset at positive sample voltages may be viewed as a valence-band edge, whereas the onset at negative voltages is caused by the drastic effect of the electric field from the tip on the tunneling barrier.