We present a detailed study of the stellar and H i structure of the dwarf irregular galaxies Sextans A and Sextans B, members of the NGC 3109 association. We use newly obtained deep (r ≃ 26.5) and wide-field g and r photometry to extend the surface brightness (SB) profiles of the two galaxies down to μV ≃ 31.0 mag/arcsec2. We find that both galaxies are significantly more extended than previously traced with surface photometry, out to ~4 kpc from their centres along their major axes. Older stars are found to have more extended distribution than younger populations. We obtain the first estimate of the mean metallicity for the old stars in Sex B, from the colour distribution of the red giant branch, ⟨[Fe/H]⟩ = -1.6. The SB profiles show signi...