Application of conversational user interfaces (CUI) or chatbots to healthcare is gaining interest fueled by the rising power of artificial intelligence, increasing popularity of mobile health applications and the desire for engagement and usability. While their use is mainly justified by increasing adherence to mobile health applications and facilitating interactions with the system, the question arises: How can such systems be evaluated in a reliable manner? This paper introduces an evaluation framework for health systems whose core interaction principle is a CUI. We derive quality dimensions and attributes by collecting relevant evaluation aspects from applications that have been developed in previous work and from literature on health chatbots. The collected aspects are aggregated into six thematic categories for chatbot quality, including user experience, linguistic, task-oriented and artificial intelligence perspectives, but also healthcare quality and system quality perspectives. The framework is intended to support developers and researchers in the domain of chatbots in healthcare in selecting relevant quality attributes to be assessed before their systems are distributed to patients.