The three-dimensional (3D) point spread function (PSF) of multilayered flat lenses was proposed in order to characterize the diffractive behavior of these subwavelength image formers. We computed the polarization-dependent scalar 3D PSF for a wide range of slab widths and for different dissipative metamaterials. In terms similar to the Rayleigh criterion we determined unambiguously the limit of resolution featuring this type of image-forming device. We investigated the significant reduction of the limit of resolution by increasing the number of layers, which may drop nearly 1 order of magnitude. However, this super-resolving effect is obtained in detriment of reducing the depth of field. Limitations exist on the formation of 3D images.