Context. The presence of stable disks around post-asymptotic giant branch (post-AGB) binaries is a widespread phenomenon. Also, the presence of (molecular) outflows is now commonly inferred in these systems. Aims. In the first paper of this series, a surprisingly large fraction of optical light was found to be resolved in the 89 Her post-AGB binary system. The data showed that this flux arises from close to the central binary. Scattering off the inner rim of the circumbinary disk, or scattering in a dusty outflow were suggested as two possible origins. With detailed dust radiative transfer models of the circumbinary disk, we aim to discriminate between the two proposed configurations. Methods. By including Herschel/SPIRE photometry, we extend the spectral energy distribution (SED) such that it now fully covers UV to sub-mm wavelengths. The MCMax Monte Carlo radiative transfer code is used to create a large grid of disk models. Our models include a self-consistent treatment of dust settling as well as of scattering. A Si-rich composition with two additional opacity sources, metallic Fe or amorphous C, are tested. The SED is fit together with archival mid-IR (MIDI) visibilities, and the optical and near-IR visibilities of Paper I. In this way we constrain the structure of the disk, with a focus on its inner rim. Results. The near-IR visibility data require a smooth inner rim, here obtained with a double power-law parameterization of the radial surface density distribution. A model can be found that fits all of the IR photometric and interferometric data well, with either of the two continuum opacity sources. Our best-fit passive models are characterized by a significant amount of ~mm-sized grains, which are settled to the midplane of the disk. Not a single disk model fits our data at optical wavelengths because of the opposing constraints imposed by the optical and near-IR interferometric data. Conclusions. A geometry in which a passive, dusty, and puffed-up circumbinary disk is present, can reproduce all of the IR, but not the optical observations of 89 Her. Another dusty component (an outflow or halo) therefore needs to be added to the system.