The field of literacy encompasses a variety of cognitive tasks, that can be categorized based on their inputs and outputs. For instance, letter denomination, word and text reading go from visual-orthographic stimuli to oral responses; spelling-to-dictation goes from acoustic stimuli to written responses. Neuroimaging data and behavioral observations support the hypothesis of shared orthographic and phonological processes and knowledge across these tasks. Unfortunately, the research field currently appears fragmented, with subdomains focusing on subsets of tasks. Further, no current computational model can simulate both reading and spelling tasks. For instance, while phonemic awareness is critical for predicting reading ability, its evaluation involves sound and word manipulation tasks beyond the scope of current computational models. As a first contribution toward the overall objective of modeling the literacy system as a whole, we introduce BRAID-Spell, a new computational probabilistic model, that extends BRAID-Acq, a model of reading and word learning. BRAID-Spell's orthographic and phonological components are symmetrical, and each can be either input or output. First, we demonstrate that using Bayes' theorem for knowledge inversion offers flexibility for defining and simulating a wide range of tasks. Second, we illustrate BRAID-Spell's capability to simulate both French word reading and spelling, and its ability to account for consistency effects in both tasks. Overall, BRAID-Spell is a new computational model with a novel approach: beyond computational models of specific tasks, it provides the first step toward a comprehensive account of the entire literacy system.