Multilayer samples of Ni/Fe and Fe/Cu/NiFe, fabricated by sputtering and characterized by transmission electron microscopy and electron diffraction, were studied by ⁵⁷Fe Mössbauer spectra and magnetization measurements. Mössbauer spectra taken in zero applied field at 300 K and 4.2 K showed midlayer and interface iron sites in Ni(20 Å)/Fe(x Å) samples with x = 20 Å, 30 Å, 50 Å, 80 Å and in-plane spin orientation. The reorientation of the magnetic moments at 4.2 K in increasing fields applied normal to the layers when combined with magnetization measurements enabled the magnetic anisotropy energy K of each sample to be evaluated. The trend of the values of K with iron layer thickness gave volume and interface anisotropy components K_V = (-5±1) × 10⁴ J m^-3 and K_S = (-0.6±0.4) × 10^-3 J m^-2 where negative values indicate in-plane preference. Similar measurements on a series of samples of Fe(30 Å)/Cu(x Å)/Ni(80%)Fe(20%)(30 Å) with x = 10 Å, 20 Å, 30 Å, 50 Å showed a tendency toward increasing in-plane anisotropy energy K with decreasing thickness of the non-magnetic Cu layer.