Population growth, consumerism and linear (take-make-dispose) economy models have been piling up waste for decades. The construction industry is also based primarily on linear economy models, but the good news is that most of the waste can be re-used or recycled. So far, numerous models for managing construction and demolition waste in a sustainable way have been developed, but only a few models have included circular economy approaches. The main objective of this study is to propose an integrated framework for the sustainability assessment of CDW management. Apart from the economic, environmental and social aspects of sustainability, this model also includes circular economy principles. The proposed framework is based on the integration of existing methods: bottom-up materials stock approximation; cost–benefit analysis for criteria calculation; and scenario and multi-criteria decision-making analysis for sustainability. It is suggested that the European average recovery rates should be used for future scenario development. With higher re-use and recycling rates, the potential for the circularity of the recovered waste grows. In an effort to increase circularity in the region, particular attention was devoted to customize the framework and examine its potential for use in the Western Balkan countries. The framework may also be useful in countries with immature construction and demolition waste management.