Molecular Hydrogen absorption spectrum

Molecular hydrogen does not begin to absorb until you get into the vacuum ultraviolet. The hydrogen atom in its ground electronic state (n=1) also does not absorb any light until you get into the vacuum ultraviolet. For the atom, the first absorption is Lyman alpha (121.5 nm). For molecular hydrogen, the first absorption is at even shorter wavelengths (ca. 110 nm).

The Balmer lines of Hydrogen atoms have n=2 as the lower state quantum number. There are hydrogen molecular states that correlate with the n=2 levels, and you do see molecular transitions that have these states as the lower state. You can't see these unless you excite the hydrogen with other means (e.g. an electric discharge).