We present near-IR narrowband continuum-subtracted images in the H-2 2.122
mu m, and Br gamma 2.166 mu m emission lines for a sample of 15 bipolar pla
netary nebulae (PNe). H-2 emission was definitely detected for most of the
objects in this sample (13 of 15). The very high H-2 detection rate support
s the idea that bipolar PNe have important reservoirs of molecular material
and offer suitable physical conditions for the excitation of H-2. The stre
ngth of the H-2 emission and the H-2/Br gamma flux ratio are found to corre
late with the morphology of the bipolar PNe observed. Bipolar PNe with broa
d and bright rings exhibit stronger H-2 emission than bipolar PNe with narr
ow twists. High-quality (subarcsec) [N II] and H alpha optical images have
been used to compare the distribution of the ionized and molecular material
. The H-2 emission lies just outside the optical [N II] emission zone.