The ratios of probabilities (the electronic branching ratios) for the rovibronic spontaneous transitions are for the first time measured for transitions from the rotational levels with J′ ≤ 6 of the I ¹∏_g ^-,v′ = 0-2 and J ¹δ_g ^-, v′ = 0 states to the vibrational-rotational levels of different low-lying electronic states B ¹∑_u ⁺, v″, J′ and C ¹∏_u ^-, v‴, J′ - 1 of the H₂ molecule (for the vibrational quantum numbers v″ ≤ 4 and v‴ ≤ 2). Values of these quantities provide a new channel of information on the internal structure of the hydrogen molecule thus far unused and should be particularly sensitive to the adiabatic values of the electronic transition dipole moments. In studying the entire set of rovibronic radiative transitions, they may significantly add to the experimental data on rovibronic terms, radiative lifetimes, and vibrational and rotational branching ratios used before. The experimental data obtained are compared to the corresponding values derived from the results of an earlier semiempirical determination and ab initio calculation of the absolute transition probabilities. Our experimental data are in remarkable agreement with the semiempirical results and significantly differ from the ab initio results. This fact directly suggests the necessity of performing more accurate ab initio calculations of the rovibronic transition probabilities for the given systems of bands.