We have developed a method to invert time-domain airborne electromagnetic (AEM) data using a parametric level-set approach combined with a conventional voxel-based technique to form a parametric hybrid inversion. The approach was designed for situations in which a voxel-based inversion alone may struggle. Such an example is where a distinct anomaly is present with sharp boundaries, and there is a large contrast between a low-resistivity target and a high-resistivity background. The first step of the proposed hybrid method used our novel parametric inversion to recover a best-fitting skewed Gaussian ellipsoid that represented the target of interest. Subsequently, the parametric result was set as an initial and reference model for the second stage, where smooth features with smaller resistivity contrasts were introduced into the model through a conventional voxel-based approach. The approach was tested with synthetic and field data. In the synthetic case, we recovered the size and dip of a conductive, thin, dipping plate with better accuracy compared with a voxel-based inversion. In the field example, we inverted AEM data over the Caber volcanogenic massive sulfide deposit. Based on information from past drilling, our results improve upon previous parametric plate inversions of the deposit itself, while additionally imaging the conductive cover over the deposit. These findings showcased how our parametric hybrid method can improve the accuracy of time-domain AEM inversions for thin dipping targets with large resistivity contrasts compared with the background.