Understanding interactions between complex human and natural systems involved in urban carbon cycling is important when balancing the dual goals of urban development to accommodate a growing population, while also achieving urban carbon neutrality. This study develops a systems breakdown accounting method to assess the urban carbon cycle. The method facilitates greater understanding of the complex interactions within and between systems involved in this cycle, in order to identify ways in which humans can adapt their interactions to reduce net greenhouse gas emissions from urban regions. Testing the systems breakdown accounting method in Stockholm County, Sweden, we find that it provides new insights into the carbon interactions with urban green-blue areas in the region. Results show how Stockholm County can reduce its emissions and achieve its goal of local carbon net-neutrality, if the green areas protect its carbon sequestration potential and maintain it to offset projected remaining active emissions. Results also show that the inland surface waters and inner archipelago waters within Stockholm County are a considerable source of greenhouse gases to the atmosphere. A better understanding of these water emissions is necessary to formulate effective planning and policy measures that can reduce urban emissions. The insights gained from this study can also be applied in other regions. In particular, water bodies could play a significant role in the urban carbon cycle and using this knowledge for more complete carbon accounting, and a better understanding of green-blue interactions could help to reduce net urban emissions in many places.