B cells are a critical component of the adaptive immune system, responsible for producing antibodies that help protect the body from infections and foreign substances. Single cell RNA-sequencing (scRNA-seq) has allowed for both profiling of B cell receptor (BCR) sequences and gene expression. However, understanding the adaptive and evolutionary mechanisms of B cells in response to specific stimuli remains a significant challenge in the field of immunology. We introduce a new method, TRIBAL, which aims to infer the evolutionary history of clonally related B cells from scRNA-seq data. The key insight of TRIBAL is that inclusion of isotype data into the B cell lineage inference problem is valuable for reducing phylogenetic uncertainty that arises when only considering the receptor sequences. Consequently, the TRIBAL inferred B cell lineage trees jointly capture the somatic mutations introduced to the B cell receptor during affinity maturation and isotype transitions during class switch recombination. In addition, TRIBAL infers isotype transition probabilities that are valuable for gaining insight into the dynamics of class switching. Via in silico experiments, we demonstrate that TRIBAL infers isotype transition probabilities with the ability to distinguish between direct versus sequential switching in a B cell population. This results in more accurate B cell lineage trees and corresponding ancestral sequence and class switch reconstruction compared to competing methods. Using real-world scRNA-seq datasets, we show that TRIBAL recapitulates expected biological trends in a model affinity maturation system. Furthermore, the B cell lineage trees inferred by TRIBAL were equally plausible for the BCR sequences as those inferred by competing methods but yielded lower entropic partitions for the isotypes of the sequenced B cell. Thus, our method holds the potential to further advance our understanding of vaccine responses, disease progression, and the identification of therapeutic antibodies.