We report on tunneling and Andreev-reflection conductance spectra of 39 K superconducting magnesium diboride, obtained with Pb and Au counter-electrodes. Two distinct steps at close to 2.7 and 7.1 meV appear in a low-resistance metallic-type Au–MgB 2 junction characteristic, whereas a tunneling-like spectrum measured for the same junction, annealed by the application of DC current, exhibits only a rounded contribution of the larger gap. Junctions with a superconducting lead counter-electrode pressed into a bulk MgB 2 sample reveal two conductance peaks that are interpreted as the result of the formation of a highly-transmitting break junctions inside the magnesium diboride ceramic. Our results strongly support the two-band model with two different gap values on quasi-two-dimensional σ (7.1 meV) and three-dimensional π (2.7 meV) Fermi surface sheets of MgB 2.