Given the significant role of universities in economic growth and social progress as well as the increasing demand for greater transparency regarding the use of public money, a valid assessment of university performance has become crucial for various stakeholders, including government, industry, funding agencies, and society at large. Contemporary assessments still focus solely on universities’ properties, thereby failing to capture their network relations. To overcome this limitation, this paper proposes a multilayer network-based method to measure the embeddedness of universities in collaboration and mobility networks. This method has several advantages: first, it is relevant for HEIs’ core missions, introducing a new dimension complementary to the existing rankings; second, it is size invariant; and last but not least, it is fully transparent. The proposed multilayer network approach enables the integration of further networks, which creates opportunities for a more comprehensive assessment of universities’ performance in achieving their core missions.