Models of the human auditory periphery range from very basic functional descriptions of auditory filtering to detailed computational models of cochlear mechanics, inner-hair cell (IHC), auditory-nerve (AN) and brainstem signal processing. It is challenging to include detailed physiological descriptions of cellular components into human auditory models because single-cell data stems from invasive animal recordings while human reference data only exists in the form of population responses (e.g., otoacoustic emissions, auditory evoked potentials). To embed physiological models within a comprehensive human auditory periphery framework, it is important to capitalize on the success of basic functional models of hearing and render their descriptions more biophysical where possible. At the same time, comprehensive models should capture a variety of key auditory features, rather than fitting their parameters to a single reference dataset. In this study, we review and improve existing models of the IHC-AN complex by updating their equations and expressing their fitting parameters into biophysical quantities. The quality of the model framework for human auditory processing is evaluated using recorded auditory brainstem response (ABR) and envelope-following response (EFR) reference data from normal and hearing-impaired listeners. We present a model with 12 fitting parameters from the cochlea to the brainstem that can be rendered hearing impaired to simulate how cochlear gain loss and synaptopathy affect human population responses. The model description forms a compromise between capturing well-described single-unit IHC and AN properties and human population response features.