Results of a room temperature polarized neutron reflectometry (PNR) study of the depth-dependent magnetization in (A)FM-coupled Fe/Si multilayers (MLs) are presented. Simultaneous interpretation of PNR data measured at increasing field values, keeping the nuclear structure of the MLs equal, shows strongly depth-dependent magnetization profiles. At low fields the Fe layers at the substrate side turn out to be predominantly ferromagnetically (FM) coupled, while an antiferromagnetic (AFM) alignment of adjacent Fe layers is observed towards the top of the MLs. When the field is increased the region of FM (AFM) alignment grows (diminishes) by rotation of the magnetization in the individual Fe layers. The overall AFM alignment is more perfect for MLs with 1.4 nm thick Si layers than for 1.1 nm thick Si layers. These observations are in excellent agreement with magneto-optical Kerr effect and vibrating sample magnetometry (VSM) investigations [1] and can be explained by growth-induced pinholes, formed predominantly in the beginning of the sputtering process.