Realistic solar magneto-convection simulations including the photospheric layers are used to study the polarization of the Fe I Zeeman-sensitive spectral lines at 6301.5, 6302.5, 15 648 and 15 652 Å. The Stokes spectra are synthesized in a series of snapshots with a mixed-polarity magnetic field whose average unsigned strength varies from = 10 to 140 G. The effects of spatial resolution and of the amount of magnetic flux in the simulation box on the profiles shapes, amplitudes and shifts are discussed. The synthetic spectra show many properties in common with those observed in quiet solar regions. In particular, the simulations reproduce the width and depth of spatially averaged Stokes I profiles, the basic classes of the Stokes V profiles and their amplitude and area asymmetries, as well as the abundance of the irregular-shaped Stokes V profiles. It is demonstrated that the amplitudes of the 1.56μm lines observed in the inter-network are consistent with a "true" average unsigned magnetic field strength of 20 G. We show that observations using these and visible lines, carried out under different seeing conditions (e.g., simultaneous observations at different telescopes), may result in different asymmetries and even opposite polarities of the profiles in the two spectral regions observed at the same spatial point.