We present a sequential data assimilation algorithm based on the ensemble Kalman inversion to estimate the near‐surface shear‐wave velocity profile and damping; this is applicable when heterogeneous data and a priori information that can be represented in forms of (physical) equality and inequality constraints in the inverse problem are available. Although noninvasive methods, such as surface‐wave testing, are efficient and cost‐effective methods for inferring an profile, one should acknowledge that site characterization using inverse analyses can yield erroneous results associated with the lack of inverse problem uniqueness. One viable solution to alleviate the unsuitability of the inverse problem is to enrich the prior knowledge and/or the data space with complementary observations. In the case of noninvasive methods, the pertinent data are the dispersion curve of surface waves, typically resolved by means of active source methods at high frequencies and passive methods at low frequencies. To improve the inverse problem suitability, horizontal‐to‐vertical spectral ratio data are commonly used jointly with the dispersion data in the inversion. In this article, we show that the joint inversion of dispersion and strong‐motion downhole array data can also reduce the margins of uncertainty in the profile estimation. This is because acceleration time series recorded at downhole arrays include both body and surface waves and therefore can enrich the observational data space in the inverse problem setting. We also show how the proposed algorithm can be modified to systematically incorporate physical constraints that further enhance its suitability. We use both synthetic and real data to examine the performance of the proposed framework in estimation of the profile and damping at the Garner Valley downhole array and compare them against the estimations in previous studies.