We demonstrated the efficacy of using a simple experimental approach, involving UV absorption spectroscopy, to monitor the transport of reactive oxygen and nitrogen species (RONS) through an agarose film (as surrogate for real tissue) into deionized (DI) water. The experiment involved placing a 4 mm thick agarose film over a quartz cuvette filled with DI water. The agarose film was exposed to a non-thermal, He atmospheric-pressure plasma jet (APPJ) and the UV absorption of the DI water was recorded in real-time. Our results indicate an accumulation of RONS within the agarose film during APPJ exposure and a subsequent time-lapsed release of RONS into the DI water. Curve fitting of the UV spectra suggested the APPJ transported and / or generated at least four RONS (NaNO₂, HNO₃, H₂O₂ and O₂) through the 4 mm thick agarose film. Our approach of analyzing the delivery depth of RONS through synthetic tissue targets might find use in the future development of APPJ medical therapies and for improving our understanding of APPJ interactions with soft tissue.