Sputtered Tb/Cr/Fe structures with a Cr layer (t(Cr)) thickness ranging from 0 to 4 nm were prepared. The coercivity (H-c) of Tb/Cr (t(Cr))/Fe films with t(Cr) >= 1 nm is consistent with that of the corresponding Cr(t(Cr))/Fe films. At the same time, the addition of the Tb layer results in a large saturation magnetization field (H-s) and even oscillatory relations of H-s on t(Cr), which might indicate an oscillatory indirect exchange coupling mediated by the spin polarization of the spacer Cr layer. Consistent oscillations are observed in anisotropic magnetoresistance (AMR) originating in spin-orbit coupling and magnetoresistance (MR) associated with interlayer exchange coupling as t(Cr) in Tb/Cr/Fe films increases. The oscillatory MR demonstrates antiferromagnetic coupling, which also implies that it is not ordinary MR, although it is of the same magnitude as a result of the nonsharp interfaces. The value of the antiferromagnetic exchange coupling J as a function of t(Cr) is estimated. Consistent oscillations with those in MR and AMR versus t(Cr) are found, accompanied by a gradually flattened oscillation for films with t(Cr) >= 2.5 nm resulting from weak coupling as the thick spacer Cr layer. Compared with the curves of MR, AMR, and J versus t(Cr), the opposite oscillations observed in the curve of H-c/H-s versus t(Cr) further confirm the oscillatory interlayer exchange coupling in the studied structure, which provides theoretical basis for the adjustment of magnetic properties in spintronics by rare earth elements.