The coherence of the spectral broadening process is the key requisite for the application of supercontinua in frequency combs. We investigate the coherence of two subsequent supercontinuum pulses created in a photonic crystal fiber pumped by a femtosecond laser. We measure Young interference fringes from a Michelson-type interferometer at different wavelengths of the output spectrum and analyze their dependence on pump intensity and polarization. The visibility of these fringes is a direct measure of the coherence of the spectral broadening processes.