We discuss ISO-SWS and ISOPHOT-S spectra of the Seyfert Galaxy NGC 4151. The spectral features in the mid-infrared are ideal tracers of the physical conditions in the narrow line emitting region (NLR), and of the spectral energy distribution (SED) of the central ionizing source. The analysis of mid-IR line profiles and the modelling of mid-IR line strengths with photoionization models are therefore powerful new tools for the study of active galactic nuclei (AGNs). We find that the mid-IR fine-structure line profiles in NGC 4151 display blue asymmetries which are very similar to those observed in the optical lines produced in the narrow line region. Because the mid-infrared lines are much less sensitive to extinction than are the optical lines this similarity places strong constraints on scenarios which have been invoked to explain the optical line asymmetries. For example, we are able to rule out the simplest radial-motion-plus-dust scenarios for the production of the line asymmetries. Our preferred model is that of a central, geometrically thin but optically thick, obscuring screen. The mid-IR line fluxes, together with a compilation of UV to near-IR narrow emission line data are used to reconstruct the spectral shape of the obscured extreme-UV continuum of the central ionizing source. We find a best-fit model - consisting of a clumpy, optically thick (ionization bounded) gas distribution - that reproduces the observed line fluxes, and which is consistent with the observed geometry of the optical NLR. The best fitting SED does not display a 'Big Blue Bump', which would be the expected signature of an accreting black hole. This is in contrast to our detection of such a bump in the SED of the Circinus Galaxy. Our analysis suggests that in NGC 4151 such a component may be absorbed by material located between the NLR and the central ionizing source.