  Context: Nearly one century after their discovery, the carrier(s) of Diffuse
Interstellar Bands 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
towards 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 use the
multi-epoch high-S/N optical spectra presented in paper I (Ma\'iz Apell\'aniz
et al. 2015), the extinction results derived there, and additional spectra.
Results: We have 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 one with a higher column density (thicker) associated with the
cluster. The first cloud has similar properties for both O-star sightlines but
the second one 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 sigma-zeta scale, some of them for the
first time. The LS III +46 12 sightline also has a high-velocity redshifted
component.
