Observations of the interstellar medium (ISM) reveal its fractal structure over a large range of scales. The quantitative description shows that the ISM consists mainly of surfaces, so that the stellar UV-radiation can deeply penetrate into the ISM and in consequence dominates its physical and chemical conditions. Thus, the bulk of the ISM can be identified as photon dominated regions (PDRs). A simple model with the proper fractal characteristics is that of an ensemble of spherical clumps with a power-law mass spectrum and a power-law mass-size relation. Hence, we model the FIR line emission of the molecular gas by the integrated emission of such an ensemble, calculating the emission of individual clumps with the KOSMA-τ PDR code. This clumpy PDR-model, with observationally constrained parameters, is fitted to the CO, [C i], and [O i] emission along the Galactic plane as observed by the FIRAS instrument abord the COBE satellite. The FIR line intensity distribution with Galactic longitude is reproduced within factors of about 2. The predicted [C ii] 158 μm line intensity and FIR continuum emission also coincide with the observations.