The orientational contribution to the third-order nonlinear response of coupled vibrational or electronic states is evaluated considering the dipole orientations of these states and molecular orientational relaxation. A general formalism is developed for calculating the third-order orientational response function for processes involving up to four distinct transition dipole moments, which are fixed in a molecular frame that is free to diffusively reorient. In particular, all tensor components of the third-order orientational response function for two coupled vibronic states were calculated as a function of the projection angle between the transition dipole moments of the fundamental transitions. The results are discussed in conjunction with specific third-order infrared nonlinear experiments on coupled vibrational systems: pump-probe, dispersed two-dimensional pump-probe, and two-dimensional photon-echo experiments. The anisotropy of the nonlinear signal and ratios of independent tensor components of the response, are shown to depend on the projection angle between the transition dipole moments and therefore can be used to access structural information about molecular systems.