  The morphological evolution of star-forming galaxies provides important clues
to understand their physical properties, as well as the triggering and
quenching mechanisms of star formation. We aim at connecting morphology and
star-formation properties of low-mass galaxies (median stellar mass $\sim$
10$^{8.5}$ M$_{\odot}$) at low redshift ($z<0.36$).
  We use a sample of medium-band selected star-forming galaxies from the
GOODS-North field. H$\alpha$ images for the sample are created combining both
spectral energy distribution fits and HST data. Using them, we mask the star
forming regions to obtain an unbiased two-dimensional model of the light
distribution of the host galaxies. For this purpose we use $\texttt{PHI}$, a
new Bayesian photometric decomposition code. We apply it independently to 7 HST
bands assuming a S\'ersic surface brightness model.
  Star-forming galaxy hosts show low S\'ersic index (with median $n$ $\sim$
0.9), as well as small sizes (median $R_e$ $\sim$ 1.6 kpc), and negligible
change of the parameters with wavelength (except for the axis ratio, which
grows with wavelength). Using a clustering algorithm, we find two different
classes of star-forming galaxies: A more compact, redder, and high-$n$ (class
A) and a more extended, bluer and lower-$n$ one (class B). We also find
evidence that the first class is more spheroidal-like. In addition, we find
that 48% of the analyzed galaxies present negative color gradients (only 5% are
positive).
  The host component of low-mass star-forming galaxies at $z<0.36$ separates
into two different classes, similar to what has been found for their higher
mass counterparts. The results are consistent with an evolution from class B to
class A. Several mechanisms from the literature, like minor and major mergers,
and violent disk instability, can explain the physical process behind the
likely transition between the classes. [abridged]
