We have investigated the infrared spectra of all 46 Herbig Ae/Be stars for which spectroscopic data are available in the ISO data archive. Our quantitative analysis of these spectra focuses on the emission bands at 3.3, 6.2, "7.7", 8.6 and 11.2 micron, linked to polycyclic aromatic hydrocarbons (PAHs), the nanodiamond-related features at 3.4 and 3.5 micron, the amorphous 10 micron silicate band and the crystalline silicate band at 11.3 micron. We have detected PAH emission in 57% of the Herbig stars in our sample. Although for most of these sources the PAH spectra are similar, there are clear examples of differences in the PAH spectra within our sample which can be explained by differences in PAH size, chemistry and/or ionization. Amorphous silicate emission was detected in the spectra of 52% of the sample stars, amorphous silicate absorption in 13%. We have detected crystalline silicate emission in 11 stars (24% of our sample), of which four (9%) also display strong PAH emission. We have classified the sample sources according to the strength of their mid-IR energy distribution. The systems with stronger mid-infared (20-100 mum) excesses relative to their near-infrared (1-5 mum) excess display significantly more PAH emission than those with weaker mid-infrared excesses. There are no pronounced differences in the behaviour of the silicate feature between the two groups. This provides strong observational support for the disk models by Dullemond et al. ( 2001), in which systems with a flaring disk geometry display a strong mid-infrared excess, whereas those with disks that are strongly shadowed by the pulled-up inner rim of the disk only display modest amounts of mid-infrared emission. Since the silicates are expected to be produced mainly in the warm inner disk regions, no large differences in silicate behaviour are expected between the two groups. In contrast to this, the PAH emission is expected to be produced mainly in the part of the disk atmosphere that is directly exposed to radiation from the central star. In this model, self-shadowed disks should display weaker PAH emission than flared disks, consistent with our observations.