The exchange bias of the soft ferromagnet mu-metal, Ni 77 Fe 14 Cu 5 Mo 4 , with the metallic antiferromagnet Fe 50 Mn 50 has been studied as a function of ferromagnet thickness and buffer layer material. Mu-metal exhibits classic exchange bias behavior: the exchange bias (H EB ) and coercive fields scale inversely with the ferromagnet's thickness, with H EB varying as the cosine of the in-plane applied field angle. While the exchange bias, coercivity, and exchange energy are greatest when the buffer layer material is (111) oriented Cu, amorphous Ta buffers allow the mu-metal to retain more of its soft magnetic character. The ability to preserve soft ferromagnetic behavior in an exchange biased heterostructure may be useful for low field sensing and other device applications.