Thick, dispersion-engineered silicon nitride is a leading platform for integrated third-order nonlinear optics, supporting supercontinuum and frequency comb generation. However, it lacks the second-order nonlinearity required by many applications. Here we bond pre-fabricated x-cut thin-film lithium niobate membranes onto finished silicon nitride waveguides as a back-end step, compatible with commercially fabricated waveguides. A single silicon nitride waveguide generates an octave-spanning supercontinuum and, through the lithium niobate membrane, concurrent second-harmonic, sum- and difference-frequency generation. These results open new possibilities for thick silicon nitride photonics, from visible light generation to on-chip f-2f comb self-referencing, a key step towards miniaturised timing and navigation quantum technologies.