We present a convenient method for determining the thickness of a cryogenic parahydrogen (pH2) solid from its infrared (IR) absorption spectrum. Millimeters-thick pH2solids of exceptional optical clarity can be produced by the rapid vapor deposition method [M.E. Fajardo and S. Tam, J. Chem. Phys. 108, 4237 (1998)]. Doping of these pH2solids is readily accomplished by co-deposition of the desired impurities, making them excellent hosts for high-resolution matrix isolation spectroscopy. The intensities of the IR “double” transitions Q1(0) + S0(0) and S1(0) + S0(0) of the pH2host are insensitive to the matrix microstructure and to the presence of dopants, so these absorptions are especially well suited for thickness determinations. We calibrate the integrated absorption intensities of these two bands against the sample thicknesses determined from transmission interference fringes appearing in the same experimental spectra; we report: α˜[Q1(0) + S0(0)] = 4.84(±0.18) × 10−14cm3/s, and α˜[S1(0) S0(0)] = 0.35(±0.02) × 10−14cm3/s (95% confidence). We also discuss several other advantages of rapid-vapor-deposited pH2solids as hosts for quantitative IR absorption spectroscopy of dopant species.