You can analytically/numerically calculate reflectance of your multi-layers and then fit the curve using an incoherent reflection model. Of course, you would need to consider both n and k.
Theoretical basis for reflectivity calculation of an individual interface are Fresnel's equations; for multilayers you need to iterate this for every interface to get the transmittance of the multilayer. As Dingkun pointed out, you need real and imaginary part of the complex refractive index, AT THE SPECIFIED WAVELENGTH, plus polarisation and angle of incidence.