The structural and magnetic properties of the evaporated Fe/V multilayers with a fixed V-layer thickness (tV = 1.5 nm) and variable Fe layer thicknesses (0.75 nm < or = tFe < or = 6 nm) have been studied by X-ray reflectivity and high-angle X-ray diffraction, conversion-electron Mössbauer spectrometry, and vibrating sample magnetometry. The results show that multilayers are formed with a broad Fe/V interface and pure crystalline bcc-Fe layers in the center of the individual subsystems. The Fe spin orientation is aligned in the film plane in the individual centers as well in the interfacial regions. The interfacial anisotropy constant Ks was estimated to be equal to 0.04 mJ/m2. This parallel magnetic anisotropy is discussed in terms of reduced symmetry effects on the hybridized 3d states.