A two-layer ceramic composite material, wherein the first predominantly load-bearing layer is an oxidic, carbon-free fiber-reinforced ceramic layer which is made by a colloidal process. The second predominantly thermally insulating layer is an oxide-ceramic foam. The colloidal process produces carbon-free oxide ceramics which, because of their high purity, have low dielectric losses in the entire usage temperature range. In addition, the colloidal process provides a simple and cost-effective production method.