Three dimensional modulation-enhanced single-molecule localization techniques, such as ModLoc, offer advancements in axial localization precision across the entire field of view and axial capture range, by applying phase shifting to the illumination pattern. However, this improvement is limited by the pitch of the illumination pattern that can be used and requires registration between separate regions of the camera. To overcome these limitations, we present ZIMFLUX, a method that combines astigmatic point-spread-function (PSF) engineering with a structured illumination pattern in all three spatial dimensions. In order to achieve this we address challenges such as optical aberrations, refractive index mismatch, supercritical angle fluorescence (SAF), and imaging at varying depths within a sample, by implementing a vectorial PSF model. In scenarios involving refractive index mismatch between the sample and immersion medium, the astigmatic PSF loses its ellipticity at greater imaging depths, leading to a deterioration in axial localization precision. In contrast, our simulations demonstrate that ZIMFLUX maintains high axial localization precision even when imaging deeper into the sample. Experimental results show unbiased localization of 3D 80 nm DNA-origami nanostructures in SAF conditions with a 1.5-fold improvement in axial localization precision when comparing ZIMFLUX to conventional SMLM methods that rely solely on astigmatic PSF engineering.