The heads of some Herbig-Haro (HH) jets have recently been detected in
emission lines of molecular species such as H-2 and CO. In this paper
we present an axisymmetric numerical simulation of an atomic, nonadia
batic jet moving into a molecular environment, from which predictions
of intensity maps in atomic/ionic and molecular emission lines can be
carried out. While the maps predicted from these models for emission l
ines of atoms and ions have the expected bow-shaped structure, the map
s for H-2 lines have a ''hole'' in the stagnation region of the bowsho
ck, where the molecules are dissociated. The morphology predicted for
the molecular emission intensity maps is in clear qualitative agreemen
t with recent observational results. We also present predictions of po
sition-velocity diagrams, which will be useful for comparisons with fu
ture long-slit spectroscopic observations of HH objects.