Phylodynamic models generally aim at jointly inferring phylogenetic relationships, model parameters, and more recently, the number of lineages through time, based on molecular sequence data. In the fields of epidemiology and macroevolution these models can be used to estimate, respectively, the past number of infected individuals (prevalence) or the past number of species (paleodiversity) through time. Recent years have seen the development of "total-evidence" analyses, which combine molecular and morphological data from extant and past sampled individuals in a unified Bayesian inference framework. Even sampled individuals characterized only by their sampling time, i.e. lacking morphological and molecular data, which we call occurrences, provide invaluable information to estimate the past number of lineages. Here, we present new methodological developments around the Fossilized Birth-Death Process enabling us to (i) incorporate occurrence data in the likelihood function; (ii) consider piecewise-constant birth, death and sampling rates; and (iii) estimate the past number of lineages, with or without knowledge of the underlying tree. We implement our method in the RevBayes software environment, enabling its use along with a large set of models of molecular and morphological evolution, and validate the inference workflow using simulations under a wide range of conditions. We finally illustrate our new implementation using two empirical datasets stemming from the fields of epidemiology and macroevolution. In epidemiology, we infer the prevalence of the COVID-19 outbreak on the Diamond Princess ship, by taking into account jointly the case count record (occurrences) along with viral sequences for a fraction of infected individuals. In macroevolution, we infer the diversity trajectory of cetaceans using molecular and morphological data from extant taxa, morphological data from fossils, as well as numerous fossil occurrences. The joint modeling of occurrences and trees holds the promise to further bridge the gap between between traditional epidemiology and pathogen genomics, as well as paleontology and molecular phylogenetics.