Electricity transmission with superconducting cables uses various cooling media. Liquid hydrogen (LH₂) is well suited for magnesium diboride (MgB₂), but the breakdown strength of LH₂-impregnated insulation has not been tested yet. In this letter, polypropylene laminated paper (PPLP) and polyimide (Kapton) insulation structures are tested in the same conditions in LH₂ and LN₂ (liquid nitrogen). The results show that Kapton presents a similar behavior for both cooling media whereas PPLP exhibits a lower shape parameter, i.e. a broader breakdown event scattering, in LH₂ than in LN₂ though scale parameters, i.e. breakdown strength at 63% cumulative probability, are similar.