Coherent interconversion between microwave and optical frequencies can serve as both classical and quantum interfaces for computing, communication, and sensing. Here, we present a compact microwave-optical transducer based on monolithic integration of piezoelectric actuators on silicon nitride photonic circuits. Such an actuator couples microwave signals to a high-overtone bulk acoustic resonator defined by the silica cladding of the optical waveguide core, suspended to enhance electromechanical and optomechanical couplings. At room temperature, this triply resonant piezo-optomechanical transducer achieves an off-chip photon number conversion efficiency of 1.6 × 10−5 over a bandwidth of 25 MHz at an input pump power of 21 dBm. The approach is scalable in manufacturing and does not rely on superconducting resonators. As the transduction process is bidirectional, we further demonstrate the synthesis of microwave pulses from a purely optical input. Capable of leveraging multiple acoustic modes for transduction, this platform offers prospects for frequency-multiplexed qubit interconnects and microwave photonics at large.