We give a model of the reconstructed process from extant taxa and the fossil record. We show that it is a nonhomogeneous birth-and-death process. Its rates are expressed from time and speciation, extinction and fossil find rates. We give a formula for the likelihood of a realization of this reconstructed process. Simulations show that fossils improve speciation and extinction rate estimates. Using the fossil record yields more detailed reconstructions of the evolutionary process than what is obtained from contemporary lineages only. In this work, we present a stochastic process modeling not only speciation and extinction, but also fossil finds. Next, we derive an explicit formula for the likelihood of a reconstructed phylogeny with fossils, which can be used to estimate the speciation and extinction rates. Finally, we provide a comparative simulation-based evaluation of the accuracy of estimations of these rates from complete phylogenies (including extinct lineages), from reconstructions with contemporary lineages only and from reconstructions with contemporary lineages and the fossil record. Results show that taking the fossil record into account yields more accurate estimates of speciation and extinction rates than considering only contemporary lineages.