The greenhouse effect is a complex scientific phenomenon that plays a crucial role in understanding climate change. Grasping students' understanding of this phenomenon on the content-specific level but also how students' conceptions are organized is vital for effective climate change education. This study addresses both levels and delves into the relationship between students' frameworks and knowledge pieces of the greenhouse effect through the analysis of multiple-choice questions, employing Bayesian correlations and multiple logistic regression. We thereby focus on specific types of conceptualizations of the greenhouse effect that have been identified in previous research and furthermore investigate the coherency of them. To do so, we analyzed answers of N = 604 grade 11 students in Austria and Germany and interpreted them from different theoretical perspectives. The findings showed that students hold various ideas about the greenhouse effect that are only seldom coherent, in particular when it comes to adequate ideas about the greenhouse effect. However, especially for a reflection-based framework of the greenhouse effect, our results demonstrate that students' conceptions show some form of coherency. We argue that our results can inform the development of effective teaching strategies that address students' existing knowledge and alternative conceptions. In terms of practical implications, the findings suggest that teaching strategies should provide opportunities for students to integrate their knowledge pieces into a more coherent understanding of the greenhouse effect. The study highlights the need for further investigation into the relationship between knowledge pieces and frameworks not only for the greenhouse effect, but for science education in general.