The transillumination window in the tissue spectrum, which extends from about 600 to about 1200 nm, is very attractive in diagnosis and therapy because the penetration of light into tissues ranges from several micrometers to several millimeters. Problems with the evaluation of red and near-IR light-tissue interaction are of great importance in the development of noninvasive blood oximetry. It is shown that it is possible to use a simplified one-dimensional (1-D) representation of such an interaction with a reliability acceptable in practice. The state of the art, taken into account here as the background, refers to the reported optical parameters of tissues when exposed to light of wavelengths included in the optical window considered. Against that background, using the arterial blood oxygen saturation as a measurement quantity, a reasonably complicated model of noninvasive processes occurring in a living object as a pulsatile inhomogeneous optical medium is presented. During the calculations and experiments, a novel use of the known transmission variant of the pulse oximetry concept is considered. At two measuring wavelengths (i.e., 660 and 940 nm), the biophysical and optical properties of living tissues are involved in relationships that include the quantities to be directly measured with known accuracy. Finally, the results of calculations referring to the transilluminated representative object (i.e., a theoretical fingertip) are compared to the appropriate results obtained during a series of measurements performed on real human subjects using the designed measuring system.