It is our duty as software engineers to understand our contribution towards sustainability and ultimately assess and improve the sustainability of the software engineering (SE) processes we apply. However, commonly established criteria for such an assessment are currently lacking. In this experience report, we share insights from our investigation into the sustainability of software engineering processes, focusing on a collaborative project with an industry partner. Our research delves into lessons learned while exploring this critical issue. Our contribution lies in the introduction of an initial framework, which includes assessment criteria as the core element, and on the results of using this framework to assess the software engineering process of our industry partner. By sharing our experiences and findings, we aim to contribute to the understanding of sustainable software engineering practices and stimulate dialogue on how software engineering can address societal and environmental challenges. Our work underscores the significance of adopting sustainable practices and encourages the software engineering community—in both academia and industry—to embrace a proactive role in advancing sustainability for society.