The lithospheric thickness and layering within the lithosphere have been previously constrained under the north American craton from various seismic tomographic studies, SKS splitting data and receiver function analyses, revealing, in particular, the presence of at least one mid-lithospheric discontinuity (MLD) with strong topography, and large variations in lithospheric thickness, not always correlated with crustal age. Building upon previous work in our group (Marone and Romanowicz, 2007; Yuan and Romanowicz, 2010; Yuan et al., 2014, EPSL), we here we present the results of several improvements to the radial and azimuthal anisotropy inversion of long period waveforms jointly with SKS splitting data. We start from our latest radially anisotropic model NASEM5 (Clouzet et al, 2018, GJI) constructed using a combination of teleseismic and regional full waveform data down to 40s period, the spectral element method for wavefield computations, and the concept of "Box Tomography" (Masson and Romanowicz, 2017), in which teleseismic and regional waveforms are combined seamlessly through the introduction of time-reversal mirrors. We have now included inversion for azimuthal anisotropy using a combination of regional long period waveforms and SKS splitting data, taking advantage, in particular, of the dense sampling afforded by the TA deployment of USArray. We have also implemented a more efficient inversion for crustal structure. We here present an updated, higher resolution radially and azimuthally anisotropic model of the north American continent, with focus on its stable and cratonic parts, and discuss its salient features in the context of models for the construction and evolution of the continental lithosphere. We probe this model under several stations at which we have independently obtained finer scale layering using a Monte Carlo Markov Chain trans-dimensional inversion approach. In this approach, 1D layered models are constrained by combining Ps converted phase waveforms and the local depth profile from a radially anisotropic shear wave tomographic model (NASEM5), rather than surface wave dispersion, as often done. In this computationally efficient method, each trial layered model is first homogeneized (i.e. Capdeville and Marigo, 2008) before comparison with the local tomographic depth profile.