This study presents a novel approach to handle structural uncertainties in the interpretation of stratigraphic structures using a transdimensional sampler, the reversible jump Markov chain Monte Carlo (RJMCMC) algorithm. Moving beyond conventional reservoir simulation models which use a fixed number of layers, the layering size is treated as variable. Hence, the number and position of model layers are unknowns to be determined by the inverse problem. The proposed method extends the application of one-dimensional RJMCMC by introducing a dip parameter, enabling the simulation of sedimentary wedges and erosional features around a well, which is not typically accounted for in standard layer-cake models used for instance in well test interpretation. To keep the model dimension low, a two-dimensional, piecewise constant permeability field is determined for each layering configuration. This inverse method, tested on a synthetic well log, facilitates robust interpretations of geological reservoir geometries and could improve the prediction of permeability spatial distribution in sedimentary settings. Demonstrating successful recovery of target models, the study opens interesting perspectives both for near-well subsurface models and full field reservoir models, and identifies the need for future work on allowing interface intersections to simulate more complex stratigraphic structures.