In this paper we present detailed models of the vertical structure (temperature and density) of passive irradiated circumstellar disks around T Tauri and Herbig Ae/Be stars. In contrast to earlier work, we use full frequency- and angle-dependent radiative transfer instead of the usual moment equations. We find that this improvement of the radiative transfer has a strong influence on the resulting vertical structure of the disk, with differences in temperature as large as 70%. However, the spectral energy distribution (SED) is only mildly affected by this change. In fact, the SED compares reasonably well with that of improved versions of the Chiang & Goldreich (CG) model. This shows that the latter is a reasonable model for the SED, in spite of its simplicity. It also shows that from the SED alone, little can be learned about the vertical structure of a passive circumstellar disk. The molecular line emission from these disks is more sensitive to the vertical temperature and density structure, and we show as an example how the intensity and profiles of various CO lines depend on the adopted disk model. The models presented in this paper can also serve as the basis of theoretical studies of e.g.�dust coagulation and settling in disks.