Complex assistive systems providing human behavior support independent of the age or abilities of users are broadly used in a variety of domains including automotive, production, aviation, or medicine. Current research lacks a common understanding of which architectural components are needed to create assistive systems that use models at runtime. Existing descriptions of architectural components are focused on particular domains, consider only some parts of an assistive system, or do not consider models at runtime. We have analyzed common functional requirements for such systems to be able to propose a set of reusable components, which have to be considered when creating assistive systems that use models. Such components constitute a reference architecture that we propose within this paper. To validate the proposed architecture, we have expressed the architectures of two assistive systems from different domains, namely assistance for elderly people and assistance for operators in smart manufacturing in terms of compliance with such architecture. The proposed reference architecture will facilitate the creation of future assistive systems.