A Rydberg molecule forms when an electron orbit of highly excited atom encompasses a ground state perturber such as another atom or molecule. This interaction between the electron and the perturber can weakly bind the two objects together. In this work we examine the Rydberg molecules formed when the ground state perturber is a diatomic molecule, specifically nitrogen oxide. Unlike an atom, a diatomic molecule has different states that respond differently to the electric fields of the Rydberg system. We examine how these internal states affect the structure of Born-Oppenheimer potentials of the Rydberg molecule.