Probabilistic inversion of airborne electromagnetic data is often approximated by a layered earth using a computationally efficient 1D kernel. If the underlying framework accounts for prior beliefs on spatial correlation, the inversion will be able to recover spatially coherent interfaces and associated uncertainties. Greenfield exploration using airborne electromagnetic data, however, often seeks to identify discrete economical targets. In mature exploration provinces, such bodies are frequently obscured by thick, conductive regolith, and the response of such economic basement conductors presents a challenge to any layered earth inversion. A well-known computationally efficient way to approximate the response of a basement conductor is to use a thin plate. Here we have extended a Bayesian parametric bootstrap approach, so that the basement of a spatially varying layered earth can contain a thin plate. The resulting Bayesian framework allowed for the inversion of basement conductors and associated uncertainties, but more importantly, the use of model selection concepts to determine if the data supports a basement conductor model or not. Recovered maps of basement conductor probabilities show the expected patterns in uncertainty; for example, a decrease in target probability with increasing depth. Such maps of target probabilities generated using the thin plate approximation are a potentially valuable source of information for the planning of exploration activity, such as the targeting of drillholes to confirm the existence of a discrete conductor in a greenfield exploration scenario. We have used a field data set from northwest Queensland, Australia, to illustrate how the approach allowed inversion for a basement conductor and related uncertainties in a spatially variable layered earth, using the information from multiple survey lines and prior beliefs of geology.