The distribution of radio continuum intensity and linear polarization has been observed with the VLA in two nearby edge-on spiral galaxies NGC 891 and NGC 4565 at 6 and 20 cm, respectively. We present here the results at a resolution of 20". The linearly polarized emission has been measured at high Z-distances of up to approximately 2 kpc, where the degree of polarization increases to over 30%. Although the distribution of polarized emission is nearly symmetric in Z about the major axis for both galaxies, a strong asymmetry about the minor axis is evident in NGC 4565 where the polarized emission at 20 cm appears mostly on the east side of the nucleus. In NGC 891 the distribution of polarized emission at 6 cm is more symmetrically disposed about the minor axis. For both galaxies, the position angle of maximum polarization is generally perpendicular to the plane of the disk. In the 6 cm data of NGC 891, an anomalous region situated at approximately 3 kpc to the northeast of the nucleus shows highly aligned magnetic fields running across the galactic disk. We present a unified model to account for the main features of the radio polarization in these two edge-on galaxies. The model geometry is determined from recent observations of face-on galaxies where the polarized emission is found to be strongest in the dark inter-arm and outer parts of the disks. We ascribe a substantial Z-thickness to this polarized emission. The asymmetries observed in the distribution of polarized emission when the model is viewed edge-on are a consequence of depolarization over the observing beam by differential Faraday rotation in an intervening plasma with randomly oriented magnetic fields. We show that the exceptionally strong wavelength dependence of this type of Faraday depolarization can result in edge-on galaxies becoming rapidly "Faraday thick" at decimeter wavelengths, thereby obliterating the polarization from regions on the far side of the disk. High-resolution radio polarization observations at several wavelengths can in fact be used together with optical emission-line maps to provide estimates of the line-of-sight average strength and distribution of the magnetic field in these galaxies. The degree of polarization observed in both galaxies increases strongly with increasing Z-distance from the plane. The low degree of polarization near Z = 0 is due to turbulent processes in the interstellar medium of the thin disk which tangle the magnetic field on scales of 100 pc. The intrinsic direction of the magnetic field in both galaxies at high Z is nearly parallel to the plane in the central regions of the disks. In NGC 891 the field lines tilt away from the plane of the galaxy at large distances along the major axis.