Interferometric single-molecule localization microscopy (iPALM, 4Pi-SMS) uses multiphase interferometry to localize single fluorophores and achieves nanometer isotropic resolution in 3D. The current data analysis workflow, however, fails to reach the theoretical resolution limit due to the suboptimal localization algorithm. Here, we develop a method to fit an experimentally derived point spread function (PSF) model to the interference 4Pi-PSF. As the interference phase is not fixed with respect to the shape of the PSF, we decoupled the phase term in the model from the 3D position of the PSF. The fitter can reliably infer the interference period even without introducing astigmatism, reducing the complexity of the microscope. Using a spline-interpolated experimental PSF model and by fitting all phase images globally, we show on simulated data that we can achieve the theoretical limit of 3D resolution, the Cramér-Rao lower bound (CRLB), also for the 4Pi microscope.