A previously presented model for generating 2D estimates of the divertor plasma conditions at JET from deuterium Balmer line intensity ratios, obtained from tomographic reconstructions of divertor camera images, was amended to consider also the Balmer emission arising from molecular processes. Utilizing the AMJUEL and H2VIRB atomic and molecular databases of EIRENE enabled also inference of the molecular divertor density from the distinguished molecularly induced emission. Analysis of a JET L-mode density scan suggests the molecularly induced emission accounting for up to 60-70% and 10-20% of the Balmer Dα and Dγ intensities, respectively, at the onset of detachment, while electron-ion recombination becomes increasingly dominant with deepening detachment. Similar observations were made by post-processing EDGE2D-EIRENE simulations, which indicated significant roles of molecular D2
+ ions and vibrational excitation of the D2 molecules as precursors for the molecularly induced emission. The inferred molecular density at the outer strike point was found to increase monotonously with decreasing strike point temperature, reaching approximately 30-50% of the local electron density at nmol,osp = 1-2×1020 m-3 at Te,osp ≈ 0.7 eV. A further steep increase by a factor of 3-5 was observed with decrease of Te,osp to 0.5 eV. The observations are in qualitative and reasonable quantitative agreement with EDGE2D-EIRENE predictions of nmol,osp within the uncertainties of the experimental data.