In this work, we demonstrate the direct observation of non-equilibrium intersubband dynamics in a modulation-doped multiple quantum well sample induced by intense terahertz pulses. The transmission spectra show a clear dependence on the incident THz field strength, which gives rise to a multitude of nonlinear optical effects that go beyond the standard textbook two-level description of light-matter interaction. Of special interest is thereby the multiple octave spanning bandwidth of the used single-cycle THz pulses, which allows the phase-locked coupling of adjacent intersubband transitions. Examples of this interaction include the efficient, coherent population transfer, the THz induced undressing of collective excitations, and the THz Stark effect.