We investigate the gravitational instability of galactic discs, treating stars and cold interstellar gas as two distinct components, and taking into account the phenomenology of turbulence in the interstellar medium (ISM), i.e. the Larson-type scaling relations observed in the molecular and atomic gas. Besides deriving general properties of such systems, we analyse a large sample of galaxies from The H I Nearby Galaxy Survey (THINGS), and show in detail how interstellar turbulence affects disc instability in star-forming spirals. We find that turbulence has a significant effect on both the inner and the outer regions of the disc. In particular, it drives the inner gas disc to a regime of transition between two instability phases and makes the outer disc more prone to star-dominated instabilities.