This paper aims to develop a semi-formal design space for Human-AI interactions, by building a set of interaction primitives which specify the communication between users and AI systems during their interaction. We show how these primitives can be combined into a set of interaction patterns which can provide an abstract specification for exchanging messages between humans and AI/ML models to carry out purposeful interactions. The motivation behind this is twofold: firstly, to provide a compact generalisation of existing practices, that highlights the similarities and differences between systems in terms of their interaction behaviours; and secondly, to support the creation of new systems, in particular by opening the space of possibilities for interactions with models. We present a short literature review on frameworks, guidelines and taxonomies related to the design and implementation of HAI interactions, including human-in-the-loop, explainable AI, as well as hybrid intelligence and collaborative learning approaches. From the literature review, we define a vocabulary for describing information exchanges in terms of providing and requesting particular model-specific data types. Based on this vocabulary, a message passing model for interactions between humans and models is presented, which we demonstrate can account for existing systems and approaches. Finally, we build this into design patterns as mid-level constructs that capture common interactional structures. We discuss how this approach can be used towards a design space for Human-AI interactions that creates new possibilities for designs as well as keeping track of implementation issues and concerns.