An accurate seismic response simulation of civil structures requires accounting for the nonlinear soil response behavior. This, in turn, requires understanding the nonlinear material behavior of in situ soils under earthquake excitations. System identification methods applied to data recorded during earthquakes provide an opportunity to identify the nonlinear material properties of in situ soils. In this study, we use a Bayesian inference framework for nonlinear model updating to estimate the nonlinear soil properties from recorded downhole array data. For this purpose, a one-dimensional finite element model of the geotechnical site with nonlinear soil material constitutive model is updated to estimate the parameters of the soil model as well as the input excitations, including incident, bedrock, or within motions. The seismic inversion method is first verified by using several synthetic case studies. It is then validated by using measurements from a centrifuge test and with data recorded at the Lotung experimental site in Taiwan. The site inversion method is then applied to the Benicia-Martinez geotechnical array in California, using the seismic data recorded during the 2014 South Napa earthquake. The results show the promising application of the proposed seismic inversion approach using Bayesian model updating to identify the nonlinear material parameters of in situ soil by using recorded downhole array data.