In 2012, the Universitat Autònoma de Barcelona initiated the Bachelor’s Degree in Primary Education – University Teaching in English (GEP-DUA), a version of the degree developed in response to the approach called Integrating Content and Language in Higher Education (ICLHE). That is, the bachelor’s degree advocated for integrated learning of the discipline’s content and a foreign language. In the case of language acquisition, the programme has prioritized the development of discourse competence in English for academic purposes. In this context, one of the teaching strategies adopted in GEP-DUA has involved the use of self-assessment and co-assessment rubrics. This paper reconstructs the process negotiated between GEP-DUA instructors and a researcher to prepare a co-assessment rubric that integrated assessment criteria both for content and for discourse, a task that proved to be highly complex. The difficulties that arose throughout the design and piloting of the assessment rubric are identified and sorted into categories, as are the opportunities created by interdisciplinary collaboration.