Tsunamis propagating along the ocean surface generate internal gravity waves which can be detected in the atmosphere and ionosphere using airglow or total electron content (TEC) measurements. Since the late 1960s, the summation of the seismic normal modes of the Earth allows to simulate the seismic ground motions measured by seismometers. We present a detailed case study of the same technique extended to the whole solid Earth–ocean–atmosphere system and show how the extended normal modes can be used to retrieve the tsunami signature not only in the ocean but also in the atmosphere and the ionosphere. On the example of the tsunami triggered by the 2012 Mw = 7.8 Haida Gwaii earthquake, we illustrate the coupling mechanisms under play and investigate in details the propagation properties of Lamb modes, atmospheric gravity modes and tsunami modes. The computed normal modes show a resonance between the tsunami modes and the atmospheric gravity modes at specific frequencies: 1.5, 2 and 2.5 mHz. We highlight that only the 1.5 mHz resonance of the tsunami modes can survive up to the ionospheric heights. Other remarkable features are also presented, such as the arrival of fundamental mode gravity waves prior to the (extended in the atmosphere) tsunami wave and the increased ocean/atmosphere coupling efficiency for larger ocean depths and during daytime. At last, for the purpose of validating the technique, we apply it to three real tsunami events and evaluate how well we quantitatively reconstruct the main features of the sea level anomaly measured by Deep-ocean Assessment and Reporting of Tsunamis buoys and the global positioning system (GPS)-derived TEC perturbation.