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Context. Spatially resolved observations of the ionized and molecular gas arecritical for understanding the physical processes that govern the interstellarmedium (ISM) in galaxies. Aims. To study the morpho-kinematic properties of theionized and molecular gas in three dusty starburst galaxies at $z = 0.12-0.17$to explore the relation between molecular ISM gas phase dynamics and thestar-formation activity. Methods. We analyse $\sim$kpc-scale ALMA CO(1--0) andseeing limited SINFONI Paschen-$\alpha$ observations. We use a dynamical massmodel, which accounts for beam-smearing effects, to constrain the CO-to-H$_2$conversion factor. Results. One starburst galaxy shows irregular morphologywhich may indicate a major merger, while the other two systems show disc-likemorpho-kinematics. The two disc-like starbursts show molecular gas velocitydispersion values comparable with that seen in local LIRG/ULIRGs, but in an ISMwith molecular gas fraction and surface density values consistent to thatreported for local star-forming galaxies. These molecular gas velocitydispersion values can be explained by assuming vertical pressure equilibrium.The star-formation activity is correlated with the molecular gas contentsuggesting depletion times of the order of $\sim 0.1-1$ Gyr. The star formationrate surface density ($\Sigma_{\rm SFR}$) correlates with the ISM pressure setby self-gravity ($P_{\rm grav}$) following a power law with an exponent closeto 0.8. Conclusions. In dusty disc-like starburst galaxies, our data supportthe scenario in which the molecular gas velocity dispersion values are drivenby the ISM pressure set by self-gravity, responsible to maintain the verticalpressure balance. The correlation between $\Sigma_{\rm SFR}$ and $P_{\rm grav}$suggests that, in these dusty starbursts galaxies, the star formation activityarises as a consequence of the ISM pressure balance.

VALES VII: Molecular and ionized gas properties in pressure balanced interstellar medium of starburst galaxies at z ~ 0.15