Background Twenty-five years ago, the need for health care interpreting in Switzerland increased due to the sharp influx of asylum seekers from war zones and countries of political unrest. Due to complex health needs, there was a need to move away from using volunteers as interpreters towards qualified interpreter services. Methods A historical qualitative case study design was used to describe the evolution of the language assistance programmes at Geneva University Hospitals, between 1992 and 2017. The aim was to map the evolution of the interpreter services against the Bilingual Health Communication Model with the constructs—Communicative Goals, Individual Agency, System Norms and Quality and Equality of Care—while identifying key factors to optimise interpreter service and patient care. Results and discussion Five phases were identified during the 25 years of service evolution studied: (1) Service initiation—the interpreter services were first used in a small service that cared for refugees and asylum seekers. (2) Growth and formalisation—due to the arrival of high numbers of Albanian-speaking asylum seekers, Albanian-speaking interpreters were provided to all departments of the Geneva University Hospitals. This helped roll out the use of interpreters among doctors and nurses. (3) Ensuring quality—the care for all patients, whether foreign-language speaking or not, became an issue and led to research into the quality of patient-provider communication. (4) Institutionalisation—this phase dealt with challenges including the lack of interpreter financing regulation and the clarification of interpreter roles. (5) Equity—healthcare interpreter services were put in an overall framework of equity standards. The Bilingual Health Communication Model was applied and showed that some items were not implemented: clear shifts (i) towards a culturally sensitive focus, (ii) towards community interpreting, (iii) towards triadic communication, (iv) towards spelling out the right to have an interpreter and (v) towards the involvement of insurance companies. Finally, the inclusion of healthcare interpreting as an essential ingredient in healthcare provision, including chronic disease management, is incomplete or missing. Conclusions Healthcare interpreting at Geneva University Hospitals has evolved from a ‘muddling-through’ approach towards an institutional approach by addressing quality of care, by focussing on the mental health of asylum seekers, training of both interpreters and users of interpreters and institutional policy based on equity.