We demonstrate supermode-based second harmonic generation in an integrated nonlinear interferometer made of linear and nonlinear directional couplers. We use a fully-fibered pump shaper to demonstrate second harmonic generation pumped by the symmetric or anti-symmetric fundamental spatial modes. The selection of the pumping mode and thus of a specific SHG spectral profile is achieved through the selection of the fundamental wavelength and via a robust phase setting scheme. We use two methods: either post-selecting or actively setting the pumping mode. Such modal phase matching paves the way for classical and quantum applications of coupled nonlinear photonic circuits, where multimode excitation, encoding and detection are a route for multiplexing and scaling up light-processing.