Metal oxide thin-film transistors are increasingly used in the driving backplanes of organic light-emitting diode displays. Commercial devices currently rely on metal oxides processed via physical vapour deposition methods, but the use of solution-based processes could provide a simpler, higher-throughput approach that would be more cost effective. However, creating oxide transistors with high carrier mobility and bias-stable operation using such processes has proved challenging. Here we show that transistors with high electron mobility (50 cm2 V−1 s−1) and operational stability can be fabricated from solution-processed multilayer channels composed of ultrathin layers of indium oxide, zinc oxide nanoparticles, ozone-treated polystyrene and compact zinc oxide. Insertion of the ozone-treated polystyrene interlayer passivates electron traps in the channel and reduces bias-induced instability during continuous transistor operation over a period of 24 h and under a high electric-field flux density (2.1 × 10−6 C cm−2). Furthermore, incorporation of the pre-synthesized aluminium-doped zinc oxide nanoparticles enables controlled n-type doping of the hybrid channels, providing additional control over the operating characteristics of the transistors.