Information embedding (IE) is the transmission of information within a host signal subject to a distortion constraint. There are two types of embedding methods, namely irreversible IE and reversible IE, depending upon whether or not the host, as well as the message, is recovered at the decoder. In irreversible IE, only the embedded message is recovered at the decoder, and in reversible IE, both the message and the host are recovered at the decoder. This paper considers combinations of irreversible and reversible IE in multiple access channels (MAC) and physically degraded broadcast channels (BC).