In this study, we examine aspects of the overall organization of bilingual conversation during talk-in-interaction among members of a close-knit family network. Code Alternation, prototypically seen as the contiguous juxtaposition of semiotic systems in such a way that the participants interpret the juxtaposition as such (Auer 1995, 116), is a common conversational practice in bilingual communities. Taking a Conversation Analytic approach as our point of departure, we analyze code alternation and code-mixing practices in naturally occurring conversations among family members of the bilingual in Greek and Turkish Muslim community of Rhodes. Firstly, we examine Greek/Turkish alternation as a conversational strategy with clear discourse functions (Auer 1995; 1998). Secondly, we see non-prototypical instances of the use of both languages in the same conversation as instances of medium negotiation or a mixed-code choice on the part of the participants (the bilingual medium or the monolectal view of code-switching, Meeuwis and Blommaert 1998; Auer 1998; Gafaranga 2007a). Last, we examine issues of identity as these can be approached based on the choices speakers of different age groups make during interaction. Based on the analysis, it is shown that, a) code alternation practices reflect not only aspects of the politics and management of the identity of the speakers as members of the same ethnic category, but also broader issues concerning the construction of youth identities as opposed to those of older generations, and b) data coming from diverse bilingual communities point to the need for greater clarity in the proposed models for the analysis of code alternation patterns.