Hydrogen has been long known for its ability to passivate defects in silicon devices. However, multiple recent studies on understanding the mechanism behind light- and elevated temperature-induced degradation (LeTID) have proposed that hydrogen plays an important role in this degradation mechanism. Despite its important role in photovoltaic applications, the quantitative assessment of hydrogen is difficult and seldom reported. In this work, we applied hydrogen effusion mass spectroscopy to quantify the hydrogen released from hydrogenated silicon nitride (SiNx:H) and atomic layer deposited (ALD) aluminum oxide (AlOx) dielectric films at elevated temperatures. We demonstrate that the amount of hydrogen effused from these layers strongly correlates with the extent of LeTID observed in the multicrystalline silicon wafers passivated with these monolayers and their stacks. It is shown that the hydrogen effusion scales linearly with the SiNx:H thickness, similar as the extent of LeTID. The effusion measurements on the AlOx/SiNx:H stack revealed that the presence of the AlOx film modifies the total amount of hydrogen that is effused, whereas it was found to slow the hydrogen in-diffusion. This result is consistent with the LeTID extent determined after contact firing where ALD AlOx layers were found to act as a hydrogen diffusion barrier, strongly reducing LeTID when placed in between c-Si and SiNx:H and increasing LeTID when placed on top of SiNx:H.