Foundation models (FMs) are a new paradigm in AI. First pretrained on broad data at immense scale and subsequently adapted to more specific tasks, they achieve high performances and unlock powerful new capabilities to be leveraged in many domains, including healthcare. This SIG will bring together researchers and practitioners within the CHI community interested in such emerging technology and healthcare. Drawing attention to the rapid evolution of these models and proposals for their wide-spread adoption, we aim to demonstrate their strengths whilst simultaneously highlighting deficiencies and limitations that give raise to ethical and societal concerns. In particular, we will invite the community to actively debate how the field of HCI - with its research frameworks and methods - can help address some of these existing challenges and mitigate risks to ensure the safe and ethical use of the end-product; a requirement to realize many of the ambitious visions for how these models can positively transform healthcare delivery. This conversation will benefit from a diversity of voices, critical perspectives, and open debate, which are necessary to bring about the right norms and best practices, and to identify a path forward in devising responsible approaches to future FM design and use in healthcare.