High-energy neutrinos produced by relativistic jets can be annihilated with thermal neutrinos emitted by the jet-associated accretion disks in gamma-ray bursts and core-collapse supernovae. For a broad range of conditions, the emerging all-flavor spectrum for neutrinos above 0.1 PeV is modified. Flavor evolution of accretion-disk neutrinos does not affect this result but can change the emerging flavor composition of high-energy neutrinos. The above effects provide potential tests of or constraints on detailed models for production of high-energy neutrinos.