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We measure directly, simultaneously, and quantitatively the absorption and scattering cross-section spectra of individual pairs of vertically stacked gold antennas resonating in the 0.9–1.6 μm wavelength regime. We find unusually different line shapes for absorption and scattering. The origin of this observation can be traced back to the interference of the scattering amplitudes of the two underlying and spectrally overlapping effective orthogonal modes of the optical-antenna pair. We speculate that such unusual line shapes should also occur in many other coupled-antenna systems.