Clusters of para-hydrogen (pH2) and ortho-deuterium (oD2) have been assembled around an OCS chromophore molecule inside He droplets in a molecular beam and studied via IR diode laser depletion spectroscopy (nu approximately 2060 cm-1). The superfluid 4He droplets provide a gentle host ensuring a constant low temperature of either T = 0.38 K for 4He droplets or T = 0.15 K for both the pure 3He and mixed 4He-3He droplets. The spectra show well resolved rotational structure of the vibrational bands for each attached hydrogen molecule in the range n = 1-8. With only one (n = 1) attached pH2, HD or an oD2 molecule the best fit rotational constants were used to determine the structure of the complex, which was found to be in surprisingly good agreement with quantum chemical calculations for the free complex. With n = 5 and 6 the Q-branch disappears for the pH2 clusters but not for the oD2 clusters which is consistent with a donut model. The moments of inertia of the pH2 and the oD2 complexes are explained by a new model in which each of the 18 attached helium atoms in a shell surrounding the OCS molecule are assigned a mass of 0.55, while each attached H2 and D2 molecule has an effective mass of about 10 and 12 u, respectively.