We have developed an analytical theory of the Schlömann spin wave generation from a ferromagnetic layer sandwiched between two semi-infinite media of another ferromagnetic material and pumped by a uniform microwave magnetic field. Our calculations show that, under identical conditions, such a non-uniformity can boost more than twice the emitted spin wave amplitude relative to that emitted from an isolated magnetic interface. The theory provides further support in favour of the dominant role played in the process by the local difference of the microwave magnetic susceptibilities of the adjacent magnetic materials.