Cosmological implications of a class of hybrid metric-Palatini gravity with a non-minimal matter-geometry coupling is considered. The theory contains a metric curvature tensor, together with a curvature tensor constructed from an independent affine connection. We will show that the model could be written as a bi-scalar–tensor gravity with a non-minimal coupling between matter sector and a scalar field. The theory will then be confronted with observational data from Cosmic Chronometers, BAO dataset from DESI and the Pantheon $$^+$$ dataset. We will show that the theory could be a good alternative to the $$\Lambda $$ CDM model with the difference that the conservation of the baryonic matter sector holds only at the background level. The statefinder analysis will also be applied to the theory and it is observed that the DE behavior of the theory exhibits a quintessence to phantom transition occurs at redshifts around $$z\approx 0.86$$ .