Integrated sensing and communication (ISAC) is expected to be one of the major features of 6G wireless networks. In an ISAC system, communications and sensing functionalities are jointly performed using the same waveform, frequency band and hardware, thereby enabling various use cases such as in cyber physical systems, digital twin and smart cities. A major challenge to the design and analysis of ISAC is a unified framework that incorporates the two distinct functions. By viewing ISAC as a type of broadcast channel, in this paper, we propose a unified ISAC framework in which communication and sensing signals are broadcast to the actual communication users and virtual sensing users. This framework allows the application of existing multiplexing schemes, such as dirty paper coding (DPC) and frequency division multiplexing (FDM) that have been intensively studied in data communications and information theory. Within this framework, we propose different superposition coding schemes, for cases when the sensing waveform is known or unknown to the communication receiver. We propose the waveform optimization algorithms in a multiple-input multiple-output (MIMO) setting accounting for the effects of clutter and Doppler shift. The proposed framework is numerically evaluated for different schemes under various sensing and communications performance metrics.