We present a detailed analysis of the complex absorption apparent in the 2-6 keV X-ray spectrum of the bright nearby Seyfert galaxy NGC 4151. We first utilize the large bandpass and medium spectral resolution afforded by BeppoSAX data to construct a 1-100 keV spectral template, which assumes the absorption arises in both warm (i.e. partially photoionized) and cold gas present in the line of sight to the active nucleus of the source. Application of this spectral model to an ASCA long-look observation of NGC 4151 reveals a partial correlation between the underlying continuum flux and the ionization state of the warm absorber. Such a correlation is an intrinsic property of a warm absorber and argues strongly in favour of this interpretation for the complex absorbing column over alternative partial covering models. The inferred relatively low density for the warm gas, implies an equilibration timescale for the dominant ions of the same order or longer than the timescale of the continuum variability. It follows that the warm component will invariably be observed in a non-equilibrium ionization state. We also find that (i) the reported hardening of the spectrum of NGC 4151 as the continuum level falls may be simply due to the presence of an underlying (hard and relatively constant) Compton-reflection component and (ii) the iron Ka line has a relatively narrow Gaussian profile and a line flux that remains constant over both short (days) and long (months to years) timescales - a relativistically broadened iron Ka feature was not required in our modelling.