© 2016 American Physical Society.A simple and yet powerful approach for modeling the structure of endohedrally confined diatomic molecules is introduced. The theory, based on a u(4) u(3) dynamical algebra, combines u(4), the vibron model dynamical algebra, with a u(3) dynamical algebra that models a spherically symmetric three-dimensional potential. The first algebra encompasses the internal rotovibration degrees of freedom of the molecule, while the second takes into account the confined molecule center-of-mass degrees of freedom. A resulting subalgebra chain is connected to the underlying physics and the model is applied to the prototypical case of H2 caged in a fullerene molecule. The spectrum of the supramolecular complex H2@C60 is described with a few parameters, and predictions for not yet detected levels are made. Our fits suggest that the quantum numbers of a few lines should be reassigned to obtain better agreement with data.