Bragg reflector structures consisting of BaF2/PbEuSe stacks have been epitaxially grown on CaF2/Si (111) substrates, The reflectors are centered at a wavelength of 4.0 mu m with a bandwidth of about 3.0 mu m. Reflectivity as high as 95% at the center wavelength has been achieved in three-stack reflectors. Cracks were visible under an optical Normarski microscope in two-stack reflectors, The formation of cracks is probably due to the accumulation of the residual thermal strain in thick layers or the hindrance of dislocation glide at the BaF2/PbEuSe interfaces.