Male Lawes's Parotia, a bird of paradise, use the highly directional reflection of the structurally colored, brilliant-silvery occipital feathers in their courtship display. As in other birds, the structural coloration is produced by ordered melanin pigmentation. The barbules of the Parotia's occipital feathers, with thickness similar to 3 mu m, contain 6-7 layers of densely packed melanin rodlets (diameter similar to 0.25 mu m, length similar to 2 mu m). The effectively similar to 0.2 mu m thick melanin layers separated by similar to 0.2 mu m thick keratin layers create a multilayer interference reflector. Reflectance measurements yielded peak wavelengths in the near-infrared at similar to 1.3 mu m, i.e., far outside the visible wavelength range. With the Jamin-Lebedeff interference microscopy method recently developed for pigmented media, we here determined the refractive index of the intact barbules. We thus derived the wavelength dependence of the refractive index of the barbules' melanin to be 1.7-1.8 in the visible wavelength range. Implementing the anatomical and refractive index data in an optical multilayer model, we calculated the barbules' reflectance, transmittance and absorptance spectra, thereby confirming measured spectra.