Mirrors for storage ring free-electron lasers in the vacuum ultraviolet must provide adequate reflectivity and resistance against synchrotron radiation. The free-electron laser system at ELETTRA (Trieste, Italy) is targeted to lase in the spectral range between 155 and 200  nm . It was demonstrated that dense oxide multilayer coatings allow lasing down to 189.9 nm. However, pure oxide systems show significant absorption at lower wavelengths and cannot be employed below 189.9 nm. Fluoride stacks can be deposited down to 130  nm with high reflection values above 95\% , but their resistance against the harsh synchrotron environment is poor. They rapidly degrade; lasing cannot be realized with this mirror approach. For the range between 170 and 190 nm , hybrid systems - combining fluoride and oxide materials - have been manufactured. With appropriate deposition procedures, mirrors achieve reflectance values up to 99\% and an adequate radiation resistance simultaneously. A mirror based on a conventional fluoride stack protected by a dense silicon dioxide protection layer was deposited and successfully employed for free-electron lasing at 176.4 nm.