In this paper we present a rigorous and general theoretical model for the illumination point spread function of a confocal microscope that correctly reproduces the optical setup. The model uses vectorial theory and assumes that monochromatic light with a Gaussian intensity distribution (such as from a laser or a single-mode fiber) is focused by a microscope objective with high numerical aperture and passes through stratified media on its way to the sample. This covers the important practical case of illumination through up to three layers, which is the situation most commonly encountered in biological microscopy (immersion oil, glass coverslip, aqueous sample medium). It also accounts for objectives that are corrected for a certain coverslip thickness and refractive index but operated under non-design conditions. Furthermore, illumination with linearly, circularly, or elliptically polarized light is covered by introducing a Babinet-Soleil compensator into the beam path. The model leads to a set of analytical equations that are readily evaluated. Two-dimensional intensity distributions for particular cases of interest are presented and discussed.