Excitation spectra of the benzene-(H-2)(n) (n = 1-3) van der Waals (vdW) complexes in the vicinity of the S-1 <-- S-0 6(0)(1) vibronic transition of the monomer were recorded with sub-Doppler resolution by utilizing mass-selective two-color resonance enhanced two photon ionization. Two distinguished isomers, correlating to para- and ortho-H-2, are identified for n = 1 and 2. This finding is the manifestation of the internal rotation of the H-2 unit(s) located above (and below) the benzene molecular plane within the complexes. For the observation of the weaker binding para species, a gas sample of pure para-H-2 was used Rotationally resolved spectra allowed us to fix the cluster geometry unambiguously. Three vibronic bands involving vdW-mode excitation were observed for the ortho species with n = 1, yielding to probable sets of vibrational frequencies of all the three vdW modes. One of them correlates to the splitting between the m = 0 and +/-1 sublevels in the j = 1 state of a freely rotating H-2 molecule, and the potential barrier for the hindered internal rotation has been evaluated from the values. Rotationally resolved spectrum of benzene-(ortho-H-2)(3) is consistent with a (2 + 1) binding motif, where two H-2 molecules on one side of the benzene plane seem to scramble their positions and roles. All the complexes examined with rotational resolution exhibited homogeneous line broadening, which corresponds to the upper state lifetimes in the subnanosecond regime, most probably due to vibrational predissociation in the S-1 6(1) manifold.