Receiver functions are a powerful tool to isolate and interpret receiver-side structure effects in teleseismic seismic records. They are easily constructed by deconvolving one component of a seismogram by another. Deconvolution is the inverse of convolution, and hence can be mathematically viewed as an inverse problem. It is a numerically unstable procedure that needs to be stabilized (i.e. regularized). This points to a recurring problem in geophysical imaging: there is a trade-off between variance and resolution, where the user needs to arbitrarily define a level of compromise. Here we propose a novel misfit function for inversion of converted phases that avoids deconvolution. In this way, the choice of regularization parameters (e.g. water level, width of a low pass filter) is avoided, and statistics of data errors can be correctly accounted for. We use this misfit measure to construct a likelihood probability function and carry out a transdimensional Bayesian inversion for shear wave structure. After illustrating the method with a synthetic test, a real data application is shown where teleseismic signals recorded at HYB station (Hyderabad, India) and surface wave dispersion measurements are jointly inverted to provide a probabilistic 1-D seismic model beneath the station. The results help address the debate on the thickness of the lithosphere in this region. We show that the sharp negative velocity jump at 110 km that was previously interpreted as the lithosphere–asthenosphere boundary (LAB) is actually a mid-lithospheric discontinuity. The actual LAB is seen deeper as a milder gradient between 150 and 200 km.