The unpolarized, helicity and transversity parton distribution functions of the nucleon are studied within a convolution model where the bare nucleon is dressed by its virtual meson cloud. Using light-front time-ordered perturbation theory, the Fock states of the physical nucleon are expanded in a series involving a bare nucleon and two-particle, meson-baryon, states. The bare baryons and mesons are described with light-front wave functions (LFWFs) for the corresponding valence-parton components. Using a representation in terms of overlap of LFWFs, the role of the non-perturbative antiquark degrees of freedom and the valence quark contribution at the input scale of the model is discussed for the leading-twist collinear parton distributions. After introducing perturbative QCD effects through evolution to experimental scales, the results are compared with available data and phenomenological extractions. Predictions for the nucleon tensor charge are also presented, finding a very good agreement with recent phenomenological extractions.