By means of the viscoelastodynamic model for a two-layer solid-fluid system and a detailed account of the locally induced acoustic radiation force, a rational analytical and computational framework is established for the viscoelastic characterization of thin tissues from high-frequency ultrasound (HFUS) measurements. For practical applications, the back-analysis is set up to interpret the frequency response function, signifying the tissue's axial displacement (captured by the imaging transducer) per squared voltage driving the 'pushing' transducer, as experimental input. On parametrizing the tissue's viscoelastic behavior in terms of the standard linear model, the proposed methodology is applied to a set of measurements performed on tissue-mimicking phantom constructs with thicknesses ranging from 0.5 to 4 mm. The results demonstrate that the model-based inversion, which carefully mimics the local boundary conditions and applied ultrasound excitation, yields viscoelastic properties for the phantom that are virtually invariant over the range of specimen thicknesses tested. Beyond its immediate application to in vitro viscoelastic characterization of thin excised tissues and tissue constructs, the proposed methodology may also find use in the characterization of skin or skin lesions over bone in vivo.