Teaching Interpersonal Communication
It's not my specialty, but I would teach interpersonal communication from the perspective of interlocutors' contrasting assumptions (including myths, biases, prejudices, and bigotries) about each other and about each other's communication styles. Such assumptions are also subject to critique in critical theory. In interpersonal communication, we see them as undermining communication, creating misunderstandings.
Power relationships are also important, if often overlooked, in interpersonal communication. Critical theory has much to say, here, about false consciousness and about asymmetries in permissions to speak, to speak forthrightly, and to demean.
Finally, interpersonal communication is largely, probably mostly, about nonverbal communication, which is subject to analysis in critical discourse analysis.