An heuristic mapping is presented that enables analysis of continuum percolation by penetrable spheres in terms of an analogous lattice model. The resulting framework is based upon the well-known Bethe lattice, which is modified by the inclusion of an adjustable proportion of fully connected subgraphs that provide a particularly simple, albeit operational, vehicle for modeling the effect of inter-particle clustering. The volume fraction at the percolation threshold is calculated as a function of (i) the degree of interpenetrability amongst the spheres, and: (ii) the extent of particle clustering, and the results are compared with findings from Monte Carlo (MC) simulations of this problem. It is found that a suitably chosen ansatz that reflects a monotonic increase in the degree of clustering with increasing inter-sphere penetrability leads to close agreement between percolation thresholds calculated using the present approach and the results of MC simulations.