Microstructural mechanisms such as domain switching in ferroelectric ceramics dissipate energy, the nature, and extent of which are of significant interest for two reasons. First, dissipative internal processes lead to hysteretic behavior at the macroscale (e.g., the hysteresis of polarization versus electric field in ferroelectrics). Second, mechanisms of internal friction determine the viscoelastic behavior of the material under small-amplitude vibrations. Although experimental techniques and constitutive models exist for both phenomena, there is a strong disconnect and, in particular, no advantageous strategy to link both for improved physics-based kinetic models for multifunctional rheological materials. Here, we present a theoretical approach that relates inelastic constitutive models to frequency-dependent viscoelastic parameters by linearizing the kinetic relations for the internal variables. This enables us to gain qualitative and quantitative experimental validation of the kinetics of internal processes for both quasistatic microstructure evolution and high-frequency damping. We first present the simple example of the generalized Maxwell model and then proceed to the case of ferroelectric ceramics for which we predict the viscoelastic response during domain switching and compare to experimental data. This strategy identifies the relations between microstructural kinetics and viscoelastic properties. The approach is general in that it can be applied to other rheological materials with microstructure evolution.