We investigate the gravitational instability of galactic discs, treatingstars and cold interstellar gas as two distinct components, and taking intoaccount the phenomenology of turbulence in the interstellar medium (ISM),i.e. the Larson-type scaling relations observed in the molecular and atomicgas. Besides deriving general properties of such systems, we analyse a largesample of galaxies from The HI Nearby Galaxy Survey (THINGS), andshow in detail how interstellar turbulence affects disc instability instar-forming spirals. We find that turbulence has a significant effect onboth the inner and the outer regions of the disc. In particular, it drivesthe inner gas disc to a regime of transition between two instability phasesand makes the outer...