Van der Waals heterostructures (vdWHs) have attracted considerable interest owing to their outstanding performances. In this study, we investigated the structural, electronic, optical, phonon transport, and thermoelectric properties of BAs-MXY vdWHs (MXY=TiSO, TiSeO, ZrSO, ZrSeO, HfSO, and HfSeO) using the density functional theory and Boltzmann transport equation. The stability of the designed vdWHs is verified based on their thermal, mechanical, and dynamic properties. Band structures explored using PBE and HSE06 functionals revealed that most vdWHs are indirect band semiconductors. The BAs-MXY vdWHs can effectively harness incident radiation. An increase in the Seebeck coefficient and electrical conductivity and a decrease in the thermal conductivity are observed with respect to temperature owing to the softening mode of phonons. The improved dimensionless figure of merit (ZT) indicates the possibility of designing BAs-MXY vdWHs for optoelectronic and thermoelectric applications.