We have developed a methodology to simultaneously invert large-scale airborne electromagnetic (AEM) survey data for conductivity and chargeability. The method is fully three-dimensional and includes full physics accounting for induced polarization and conductivity. The full dimensionality allows for the inclusion of inline, vertical, and cross-line components of the EM field in the inversion. This reduces non-uniqueness in the inverse models and avoids distortions due to 1D approximations. Accounting for the chargeability increases the accuracy of the recovered conductivity and allows for an additional physical parameter to aid in interpretation. The computer implementation of the method is based on the moving sensitivity domain approach, which enables the user to invert the large-scale geophysical survey data without losing resolution. The method has been used to interpret a large variety of AEM data acquired by different modern airborne systems. We demonstrate the efficacy of the developed technique of simultaneous 3D inversion of AEM data in two case studies using VTEM and TEMPEST data.