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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. In this paper, combinations of irreversible and reversible IE in multiple access channels (MAC) and physically degraded broadcast channels (BC) are considered. In this paper, MAC IE in which separate encoders embed their messages into their host signals subject to distortion constraints is considered. The embedded signals from the two encoders are transmitted to a single decoder across a MAC. For the MAC IE model, the following three cases are considered: A) no host recovery at the decoder, B) lossless recovery of one host at the decoder, and C) lossless recovery of both hosts at the decoder. For the cases A and B, inner bounds on the respective capacity regions are developed. For the case C, inner and outer bounds on the capacity region are developed, and the capacity region is obtained if the hosts are independent. In this paper, BC IE in which two messages intended for separate decoders are embedded into a given host sequence by a single encoder subject to a distortion constraint is also considered. For the BC IE model, the following four cases are considered: A') lossless recovery of the host sequence at neither of the decoders, B') lossless recovery of the host sequence at only the better decoder, C') lossless recovery of the host sequence at both decoders, and D') lossless recovery of the host sequence at only the worse decoder. For cases A' and B', inner and outer bounds on the respective capacity regions are developed. For cases C' and D', the identical capacity regions are obtained.