Spontaneous emission of an atom with two close upper levels arid one lower level in a multilayer dielectric medium, and quantum interference between transitions form the upper leves to the lower one, are considered. Since the medium is inhomogeneous along the direction normal to tbe interfaces of the dielectric layers, the vancuum had an anisotropic spatial structure, and quantum interference between the two decay channels can appear even if the two dipole matrix elemeats are ortbogonal to each other. If the atom is pLaced in a three-layer dielectric plate cavity, a strong quantum interference interference similar to that for an atom with two nearly parallel dipole moments in free space arises due to the influence of anisotropic of anisotropic vacuum. Putting the atom in a three-layer dielectric waveguide and a one-dimensional photonic crystal, there appears a strong quantum interference similar to that for an atom with nearly antiparallel dipole moments.