NGC 4330 is one of the Virgo galaxies whose UV emission distributions show a tail structure. An associated tail structure is also observed in the HI and Hα emission distributions. Previous dynamical modeling has shown that the galaxy is approaching the cluster center and is therefore undergoing increasing ram pressure stripping. Recent stellar population fitting of deep optical spectra together with multiband photometry led to the determination of the time when star formation was quenched in the galactic disk. We introduce a new version of the dynamical model that includes not only the dense neutral gas, but also the diffuse ionized gas, and we aim to reproduce the HI, Hα, and UV distributions together with the star formation histories of the outer gas-free parts of the galactic disk. We present the results of 50 simulations with five different Lorentzian temporal ram pressure profiles and five different delays between the simulation onset and peak ram pressure. The delays were introduced to study the influence of galactic structure on the outcome of the simulations. The inclusion of diffuse gas stripping significantly changes the HI, UV, and Hα emission distributions. The simulations with diffuse gas stripping naturally led to vertical low surface density filaments in the downwind region of the galactic disk. These filaments occur less frequently in the simulations without diffuse gas stripping. The simulations with diffuse gas stripping led to better joint fits to the spectral energy distributions (SEDs) and optical spectra. The HI, near-UV, and Hα morphologies of the model snapshots that best reproduce the SEDs and optical spectra are sufficiently different to permit a selection of best-fit models. We conclude that the inclusion of diffuse gas stripping significantly improves the resemb+lance between the model and observations. Our preferred model yields a time to peak ram pressure of 140 Myr in the future. The spatial coincidence of the radio continuum and diffuse Hα tails suggests that both gas phases are stripped together. We suggest that the star formation in the outer tail is sporadic and low level, and this explains the absence of a significant amount of cosmic ray electrons there. Furthermore, we suggest that the mixed interstellar medium is ionized by collisions with the thermal electrons of the ambient intracluster medium, which confines the filaments.