The lattice model proposed by Denning in her seminal work provided secure information flow analyses with an intuitive and uniform mathematical foundation. Different organisations, however, may employ quite different security lattices. In this paper, we propose a connection framework that permits different organisations to exchange information while maintaining both security of information flows as well as their autonomy in formulating and maintaining security policy. Our prescriptive framework is based on the rigorous mathematical framework of Lagois connections given by Melton, together with a simple operational model for transferring object data between domains. The merit of this formulation is that it is simple, minimal, adaptable and intuitive, and provides a formal framework for establishing secure information flow across autonomous interacting organisations. We show that our framework is semantically sound, by proving that the connections proposed preserve standard correctness notions such as non-interference.