We report NMR studies of the orientational ordering of molecular hydrogen in films physisorbed on hexagonal boron nitride (BN). The local orientational ordering of the molecular axes is determined for both thick films (12 layers) and thin films (bilayers). The ordering observed is in both cases very different from that observed for bulk solid hydrogen. Quadrupolar glass ordering occurs for intermediate layers in thick films at low ortho concentrations $0.25<X<0.40$ and $T<~0.7\mathrm{K}$. The ortho molecules remain rotationally disordered in the outer layers of the thick films and invariant to small changes in thickness. In the bilayers one observes a long range ordering for $T<~1.95 \mathrm{K}$ and $X<~0.56$, and a quadrupolar glass ordering for intermediate concentrations $(0.37<X<0.55)$ and intermediate temperatures $(0.7<T<1.1 \mathrm{K})$.