Conceptual understanding is one of the main topics in science and physics education research. In the majority of conceptual understanding studies, students' understanding levels were categorized dichotomously, either as alternative or scientific understanding. Although they are invaluable in many ways, namely developing new instructional materials and assessment instruments, students' alternative understandings alone are not sufficient to describe students' conceptual understanding in detail. This paper introduces an example of a study in which a method was developed to assess and describe students' conceptual understanding beyond alternative and scientific understanding levels. In this study, six undergraduate students' conceptual understanding levels of direct current electricity concepts were assessed and described in detail by using their answers to qualitative problems. In order to do this, conceptual understanding indicators are described based on science and mathematics education literature. The students' understanding levels were analysed by assertion analysis based on the conceptual understanding indicators. The results indicated that the participants demonstrated three intermediate understanding levels in addition to alternative and scientific understanding. This paper presents the method and its application to direct current electricity concepts.