Universities globally are called to educate collaborative and ethical engineers. In response, interdisciplinary problem-based learning is increasingly used to equip students with competencies needed to solve grand societal challenges. However, complex problem-solving in interdisciplinary teams can challenge students' existing beliefs and cause confusion. Our study examines these challenges through the lens of 'disorienting dilemmas' from transformative learning theory and investigates students' coping strategies. Through twenty-nine student interviews, we uncovered disorienting dilemmas related to self-identity, problem-solving, disciplinary perceptions, conceptual understanding, and collaboration. Additionally, based on varied cognitive and behavioural responses, we identified four coping strategies: integrating, investigating, negotiating, and withdrawing. Notably, we observed shifts in students' use of coping strategies. Our research advances transformative learning theory through its focus on shared learning and the recognition of diversity of coping strategies, thus providing insights for designing supports that guide students towards more constructive strategies and facilitate transformative learning.