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 \simeq 26.5 ) and wide field g , r photometry to extend the Surface Brightness ( SB ) profiles of the two galaxies down to \mu _ { V } \simeq 31.0  mag/arcsec ^ { 2 } . We find that both galaxies are significantly more extended than what previously traced with surface photometry , out to \sim 4  kpc from their centers along their major axis . Older stars are found to have more extended distribution with respect to younger populations . We obtain the first estimate of the mean metallicity for the old stars in Sex B , from the color distribution of the Red Giant Branch , \langle [ Fe / H ] \rangle = -1.6 . The SB profiles show significant changes of slope and can not be fitted with a single Sersic model . Both galaxies have HI discs as massive as their respective stellar components . In both cases the H i  discs display solid-body rotation with maximum amplitude of \sim 50  km s ^ { -1 } ( albeit with significant uncertainty due to the poorly constrained inclination ) , implying a dynamical mass \sim 10 ^ { 9 } ~ { } M _ { \sun } , a mass-to-light ratio \frac { M } { L _ { V } } \sim 25 and a dark-to-barionic mass ratio of \sim 10 . The distribution of the stellar components is more extended than the gaseous disc in both galaxies . We find that the main , approximately round-shaped , stellar body of Sex A is surrounded by an elongated low-SB stellar halo that can be interpreted as a tidal tail , similar to that found in another member of the same association ( Antlia ) . We discuss these , as well as other evidences of tidal disturbance , in the framework of a past passage of the NGC 3109 association close to the Milky Way , that has been hypothesized by several authors and is also supported by the recently discovered filamentary configuration of the association itself .