The quantum superposition principle has been extensively utilized in the quantum mechanical description of the bonding phenomenon. It explains the emergence of delocalized molecular orbitals and provides a recipe for the construction of near-exact electronic wavefunctions. On the other hand, its existence in composite systems may give rise to nonclassical correlations that are regarded now as a resource in quantum technologies. Here, we approach the electronic ground states of three prototypical molecules from the point of view of fermionic information theory. For the first time in the literature, we properly decompose the pairwise orbital correlations into their classical and quantum parts in the presence of superselection rules. We observe that quantum orbital correlations can be stronger than classical orbital correlations though not often. Also, quantum orbital correlations can survive even in the absence of orbital entanglement depending on the symmetries of the constituent orbitals. Finally, we demonstrate that orbital entanglement would be underestimated if the orbital density matrices were treated as qubit states.