Two-dimensional vibrational spectroscopy has been used to characterize transient molecular structure by measuring the couplings and projection angles between two strongly coupled anharmonic vibrations. Two-dimensional Fourier-transform infrared spectra of the coupled carbonyl stretches of Rh(CO)(2)(C5H7O2) in hexane have been obtained from femtosecond vibrational echo signals detected with spectral interferometry. The eight resonances in the two-dimensional spectrum can be interpreted as two diagonal peaks and two cross peaks, each split into a pair. The splitting between the peak pairs is directly related to the diagonal and off-diagonal anharmonicity of the symmetric and asymmetric carbonyl stretches. The ratio of the amplitude of the cross peaks for two different polarization geometries determines the projection angle between the coupled transition dipoles. The experimental characterization of the vibrational eigenstates allows the local carbonyl structure to be modeled as bilinearly coupled cubic anharmonic oscillators. The interaction between the carbonyl stretches arises from the mutual bonding with the rhodium metal center. This two-dimensional infrared experiment characterizes the structure with a time window of roughly 20 ps, suggesting a general method for capturing transient molecular structure in solution.