For the first time branching ratios for various rotational branches and v"-progressions of 10 band systems (including those forbidden in adiabatic approximation) emitted in the transitions from single rovibronic levels of singlet and triplet 3d term complexes of H_2 and D_2 have been measured (more than 300 branching ratios). Remarkable differences (often more than order of magnitude) are observed between experimental branching ratios and those calculated in the framework of adiabatic approximation: Honl-London formulae for electronic-rotational and Franck-Condon approximation for electronic-vibrational transitions. Non-adiabatic theoretical model taking into account electronic-rotation and electronic-vibrational coupling is developed which does not need smallness of the perturbation. Absolute rovibronic transition probabilities and radiative lifetimes of upper rovibronic levels of 17 band systems of H_2 and D_2 are obtained semiempirically. For the first time the direct comparison is made of the ab initio calculated transition probabilities with those obtained from the experimental data. It should be underlined that those calculations are most precise now and they have been performed due to our request by world-famous groups of prof.L.Wolniewicz (Poland) and K.Dressler (Switzeland). The data obtained in present work were used for spectroscopical diagnostics of non-equilibrium plasma generated by capillary-arc (St.-Petersburg State University, Russia), RF and bucket (in cooperation with Prof.F.Doebele, Uni-Essen,BRG) and microwave (in coop. with Dr.J.Roepcke, INP-Greifswald,BRG) low pressure discharges in hydrogen and hydrogen-rare gas mixtures.