By molecular beam epitaxy we have grown a quarter‐wave stack of lattice‐matched Al0.1Ga0.9As/Ca0.45Sr0.55F2 multilayer heterostructures which has high reflectivity (89%) over a broad spectral range. Unlike similar structures of (Al,Ga)As/GaAs which require many periods to achieve high reflectivity, the III‐V/fluoride structures require only four periods due to the large difference in the refractive indices of the III‐V compound and the fluoride (3.6 and 1.4 at 0.9 μm, respectively). Furthermore, for the (Al,Ga)As/GaAs structures the high‐reflectivity plateau is narrower, and because of absorption in the GaAs layers the reflectivity decreases rapidly at wavelengths shorter than the band‐gap wavelength of GaAs. For the III‐V/fluoride structures grown the absorption is not a problem, and the high‐reflectivity region extends from 0.9 μm to 0.7 μm. The ability to grow epitaxial fluoride and (Al,Ga)As with arbitrary AlAs mole fraction, and therefore different refractive indices, should stimulate interesting applications in optics.