We jointly invert local fundamental-mode and higher-order surface-wave phase-velocities for radial models of the thermo-chemical and anisotropic physical structure of the Earth's mantle to similar to 1000 km depth beneath the North American continent. Inversion for thermo-chemical state relies on a self-consistent thermodynamic method whereby phase equilibria and physical properties (P-, S-wave velocity and density) are computed as functions of composition (in the Na2O-CaO-FeO-MgO-Al2O3-SiO2 model system), pressure and temperature. We employ a sampling-based strategy to solve the non-linear inverse problem relying on a Markov Chain Monte Carlo method to sample the posterior distribution in the model space. A range of models fitting the observations within uncertainties are obtained from which any statistics can be estimated. To further refine sampled models we compute geoid anomalies for a collection of these and compare with observations, exemplifying a posteriori filtering through the use of additional data. Our thermo-chemical maps reveal the tectonically stable older eastern parts of North America to be chemically depleted (high Mg#) and colder (>200 degrees C) relative to the active younger regions (western margin and oceans). In the transition zone the thermo-chemical structure decouples from that of the upper mantle, with a relatively hot thermal anomaly appearing beneath the cratonic area that likely extends into the lower mantle. In the lower mantle no consistent large-scale thermo-chemical heterogeneities are observed, although our results do suggest distinct upper and lower mantle compositions. Concerning anisotropy structure, we find evidence for a number of distinct anisotropic layers pervading the mantle, including transition zone and upper-most lower mantle.