During speech development, babies learn to perceive and produce speech units, especially syllables and phonemes. However , the mechanisms underlying the acquisition of speech units still remain unclear. We propose a Bayesian model of speech communication, named "COSMO SylPhon", for studying the acquisition of both syllables and phonemes. In this model, speech development involves a sensory learning phase, mainly concerned with perception development, and a motor learning phase, mainly concerned with production development. We study how an agent can learn speech units during these two phases through an unsupervised learning process based on syllable stimuli. We show that the learning process enables to efficiently learn the distribution of syllabic stimuli provided in the environment. Importantly, we show that if agents are equipped with a bootstrap process inspired by the Frame-Content Theory of speech development, they learn to associate consonants to specific articulatory gestures, providing the basis for consonantal articulatory invariance.