This study devises a novel hybrid public-transit service that uses modular autonomous vehicles (MAVs) coupled in one fleet that travels a fixed base route. MAVs can decouple from the fleet at the beginning of selected road segments and recouple to the fleet at the end of these segments. This allows a decoupled MAV to serve passengers who request door-to-door service within the deviated area, while the other passengers complete their trips via regular service. This study develops an optimisation model to determine the deviated segments, the MAVs to be decoupled and the corresponding timetable that minimises the total passenger and operator costs. Finally, a case study is conducted using real data from Dalian, China. The results show that compared with a conventional fixed-route service, the hybrid service significantly reduces the total system cost, especially passenger walking and waiting time costs.