The anomalously small jumps in specific heat, ΔC, of superconducting lanthanum and yttrium compounds are discussed in terms of Suhl, Matthias and Walker's theory of superconductivity in the case of overlapping two bands. It turns out that the law of corresponding states still holds in a generalized sense. The ratio between the jump and the electronic specific heat in the normal phase at the transition temperature, ΔC/γTc, is a function of four independent quantities, although the theory contains five parameters. The ratio is found to be generally smaller than the BCS result, 1.43, for superconductors with a single conduction band. It is suggested that electron tunneling experiments could determine the two energy gaps at the absolute zero temperature and the ratio between them at the transition temperature, thereby providing sufficient knowledge to estimate the ratio. The experimental results for niobium and molybdenum are discussed. Niobium does not show such a small ratio and is suggested to have rather strong pairing interactions. Molybdenum is a weak coupling superconductor and has a small ratio ΔC/γTc. In one of the Appendices, a derivation is presented of the electron tunneling characteristics at non-zero temperatures, the time variation in the density matrix being explicitly taken into account.