This paper studies the effects of an embedded and distributed inhomogeneity on the underwater sound radiation from an elastically coated plate. Embedding a signal conditioning plate (SCP) in the coating material provides an extra parameter for controlling the sound radiation of the plate, as compared with the previous design with an SCP on the coating surface [Y. Zhang and J. Pan, J. Acoust. Soc. Am. 133(1), 173-185 (2013)]. For such a configuration, the vibration and sound responses of the coated plate to a point force excitation are described by three coupled Fredholm integral equations of the second kind. Its acoustical properties are examined by comparing the radiation powers from plates without an SCP, with a surface SCP, and with an embedded SCP. The differences in the sound powers are explained through resonance and scattering caused by the interaction of the embedded SCP with structural waves. The effects of the depth of the embedded SCP in the coating material on the sound radiation properties of the plate are discussed in detail.