Wave propagation, a key area in seismology, plays a crucial role in fields such as mineral exploration, hydrocarbon detection, and infrastructure development. Therefore, this study investigates the propagation of plane waves in a homogeneous, isotropic, generalized micropolar viscothermoelastic medium under the influence of viscosity, the hyperbolic two-temperature (HTT) parameter, and impedance boundary conditions. By deriving and reducing the governing equations to two dimensions and transforming them using dimensionless quantities and potential functions, the present model captures the combined effects of thermal, viscous, and micropolar interactions. The analysis further incorporates impedance parameters at the boundaries to simulate realistic reflection scenarios relevant to acoustics, seismology, and advanced material design. Amplitude ratios of various reflected waves are obtained by applying the reflection technique along with appropriate boundary conditions. Numerical simulations, based on the material properties of magnesium crystal, illustrate the effects of the HTT parameter, viscosity, and impedance on wave propagation. The results reveal that both viscosity and the HTT parameter significantly influence the amplitude and attenuation of reflected waves, with distinct trends observed for different wave types. Some special and limiting cases are also identified, offering a comprehensive theoretical framework that bridges classical and advanced models of wave propagation in complex media. The findings are particularly relevant to seismology, non-destructive testing, and the development of advanced materials for aerospace and geophysical applications.