The magnetic and structural properties of ion-beam-sputtered Fe/FeCrB and Fe/CoNbZr multilayers were studied as a function of the FeCrB and CoNbZr layer thicknesses. Good soft-magnetic properties (coercivity <60 A/m and permeability >1000) are obtained only when Fe grains are small, which requires, on the one hand, multilayers with Fe layer thicknesses below 10 nm and, on the other hand, FeCrB interlayers with thicknesses above 1 nm or CoNbZr interlayers with thicknesses above 3 nm. In this case interlayers are amorphous, which induces repeated nucleation of Fe grains. Only at FeCrB thicknesses of 1 nm are the interlayers crystalline due to interface mixing. This in contrast to CoNbZr interlayers which in addition grow epitaxially in a crystalline structure up to thicknesses of 3 nm. When interlayers are crystalline columnar growth of Fe results. As a consequence coercivity increases and permeability decreases.