Scanning Acoustic Microscopy (SAM) emerges as a versatile label-free imaging technology with broad applications in biomedical imaging, non-destructive testing, and material research. This article presents a framework for the estimation of stochastic impedance through SAM, with a particular focus on its application to the salmon fish scale. The framework leverages uncertain reflectance, marking its pioneering application to uncertainty quantification in the acoustic impedance of fish scales through acoustic responses. The study uses maximal overlap discrete wavelet transform, to decompose acoustic responses effectively and is further processed to predict the acoustic impedance. To establish the effectiveness of the proposed framework, well-known materials like a pair of target medium (polyvinylidene fluoride) and reference medium (polyimide) are employed for impedance characterization. Results demonstrate over 90%accuracy in PVDF impedance estimation, validating the framework. A stochastic impedance map, using Kriging with a Gaussian variogram, offers insights into the complex biomechanics of a fish’s scale.