In a multilayer mirror (1) for the reflection of EUV radiation containing a large number of alternating molybdenum layers (4) and silicon layers (3), a barrier layer (5) containing a silicon nitride or a silicon boride is included at a number of interfaces between the molybdenum layers (4) and the silicon layers (3). As a result of the barrier layers (5) of a silicon nitride or of a silicon boride, high thermal stability is achieved, in particular high long-term stability at temperatures of more than 300° C., whilst at the same time achieving high reflectivity in the multilayer mirror. A multilayer mirror (1) of this type can, in particular, be used as a heatable collector mirror for an EUV radiation source.