In conductor-insulator composites in which the conducting particles are dispersed in an insulating continuous matrix the electrical connectedness is established by interparticle quantum tunneling. A recent formulation of the transport problem in these kinds of composites treats each conducting particle as electrically connected to all others via tunneling conductances to form a global tunneling network. Here, we extend this approach to nonhomogeneous composites with a segregated distribution of the conducting phase. We consider a model of segregation in which large random insulating spherical inclusions forbid small conducting particles to occupy homogeneously the volume of the composite, and allow tunneling between all pairs of the conducting objects. By solving numerically the corresponding tunneling resistor network, we show that the composite conductivity σ is enhanced by segregation and that it may remain relatively large also for very small values of the conducting filler concentration. We interpret this behavior by a segregation-induced reduction of the interparticle distances, which is confirmed by a critical path approximation applied to the segregated network. Furthermore, we identify an approximate but accurate scaling relation permitting us to express the conductivity of a segregated systems in terms of the interparticle distances of a corresponding homogeneous system, and which provides an explicit formula for σ which we apply to experimental data on segregated RuO2-cermet composites.