In recent years, mapping tissue microstructure in the cortex using high gradient diffusion MRI has received growing attention. The Soma And Neurite Density Imaging (SANDI) explicitly models the soma compartment in the cortex assuming impermeable membranes. As such, it does not account for diffusion time dependence due to water exchange in the estimated microstructural properties, as neurites in gray matter are much less myelinated than in white matter. In this work, we performed a systematic evaluation of an extended SANDI model for in vivo human cortical microstructural mapping that accounts for water exchange effects between the neurite and extracellular compartments using the anisotropic Kärger model. We refer to this model as in vivo SANDIX, adapting the nomenclature from previous publications. As in the original SANDI model, the soma compartment is modeled as an impermeable sphere due to the much smaller surface-to-volume ratio compared to the neurite compartment. A Monte Carlo simulation study was performed to examine the sensitivity of the in vivo SANDIX model to sphere radii, compartment fractions, and water exchange times. The simulation results indicate that the proposed in vivo SANDIX framework can account for the water exchange effect and provide measures of intra-soma and intra-neurite signal fractions without spurious time-dependence in estimated parameters, whereas the measured water exchange times need to be interpreted with caution. The model was then applied to in vivo diffusion MRI data acquired in 13 healthy adults on the 3-Tesla Connectome MRI scanner equipped with 300 mT/m gradients. The in vivo results exhibited patterns that were consistent with corresponding anatomical characteristics in both cortex and white matter. In particular, the estimated water exchange times in gray and white matter were distinct and differentiated between the two tissue types. Our results show the SANDIX approach applied to high-gradient diffusion MRI data achieves cortical microstructure mapping of the in vivo human brain with the evaluation of water exchange effects. This approach potentially provides a more appropriate description of in vivo cortical microstructure for improving data interpretation in future neurobiological studies.