Fe whisker/Cr/Fe(001) samples can be prepared in a nearly perfect layer by layer growth. It will be shown that the initial reversal of the phase in the short wavelength oscillations of the interlayer exchange coupling is most likely caused by the presence of interface alloying at the Fe/Cr interface. The ability to grow nearly perfect layers of Mn between Cr and Fe layers allows one to investigate the role of a strong intrinsic antiferromagnet, Mn, on the exchange coupling through the weak antiferromagnetic spin density wave in Cr. It will be shown that the Mn layers do not affect the sign of the interlayer exchange coupling. The sign of the exchange coupling is given by the number (parity) of pure Cr atomic layers. These results are consistent with recent theoretical calculations that predict the BCT Mn on Fe is antiferromagnetic with fully compensated (001) atomic planes.