Context. Nearly one century after their discovery, the carrier or carriers of diffuse interstellar bands (DIBs) is/are still unknown and there are few sightlines studied in detail for a large number of DIBs. Aims: We want to study the ISM sightlines toward LS III +46 11 and LS III +46 12, two early-O-type stellar systems, and LS III +46 11 B, a mid-B-type star. The three targets are located in the stellar cluster Berkeley 90 and have a high extinction. Methods: We used the multiepoch high-S/N optical spectra presented in Paper I, the extinction results derived there, and additional spectra. Results: We measured equivalent widths, velocities, and FWHMs for a large number of absorption lines in the rich ISM spectrum in front of Berkeley 90. The absorbing ISM has at least two clouds at different velocities, one with a lower column density (thinner) in the K i lines located away from Berkeley 90 and another with a higher column density (thicker) associated with the cluster. The first cloud has similar properties for both O-star sightlines, but the second is thicker for LS III +46 11. The comparison between species indicate that the cloud with a higher column density has a denser core, allowing us to classify the DIBs in a σ-ζ scale, some of these for the first time. The LS III +46 12 sightline also has a high-velocity redshifted component.