  We study the behavior of eight diffuse interstellar bands (DIBs) in different
interstellar environments, as characterized by the fraction of hydrogen in
molecular form [$f$(H$_2$)], with comparisons to the corresponding behavior of
various known atomic and molecular species. The equivalent widths of the five
"normal" DIBs ($\lambda\lambda$5780.5, 5797.1, 6196.0, 6283.8, and 6613.6),
normalized to $E(B-V)$, show a "Lambda-shaped" behavior: they increase at low
$f$(H$_2$), peak at $f$(H$_2$) ~ 0.3, and then decrease. The similarly
normalized column densities of Ca, Ca$^+$, Ti$^+$, and CH$^+$ also decline for
$f$(H$_2$) > 0.3. In contrast, the normalized column densities of Na, K, CH,
CN, and CO increase monotonically with $f$(H$_2$), and the trends exhibited by
the three C$_2$ DIBs ($\lambda\lambda$4726.8, 4963.9, and 4984.8) lie between
those two general behaviors. These trends with $f$(H$_2$) are accompanied by
cosmic scatter, the dispersion at any given $f$(H$_2$) being significantly
larger than the individual errors of measurement. The Lambda-shaped trends
suggest the balance between creation and destruction of the DIB carriers
differs dramatically between diffuse atomic and diffuse molecular clouds;
additional processes besides ionization and shielding are needed to explain
those observed trends. Except for several special cases, the highest
$W$(5780)/$W$(5797) ratios, characterizing the so-called "sigma-zeta effect",
occur only at $f$(H$_2$) < 0.2. We propose a sequence of DIBs based on trends
in their pair-wise strength ratios with increasing $f$(H$_2$). In order of
increasing environmental density, we find the $\lambda$6283.8 and
$\lambda$5780.5 DIBs, the $\lambda$6196.0 DIB, the $\lambda$6613.6 DIB, the
$\lambda$5797.1 DIB, and the C$_2$ DIBs.
