Empirical bond-order potential (BOP) with the aid of ab initio calculations is applied to investigate structures and miscibility of BxAl1-xN and BxGa1-xN alloys with 3-fold coordinated hexagonal (Hex) and 4-fold coordinated wurtzite (WZ) structures. We find that the Hex structure is stabilized for free-standing BxAl1-xN and BxGa1-xN alloys with boron composition x >= 0.9 while the WZ structure is favorable for BxAl1-xN (BxGa1-xN) alloy with lattice constraint of AlN (GaN) over the entire boron composition range. Furthermore, we reveal that the miscibility of BxAl1-xN and BxGa1-xN alloys with Hex structure is lower than that with WZ structure due to the relaxation of atoms within in-plane directions in Hex structure. These results suggest that our approach using BOP is feasible to clarify stability and miscibility of BxAl1-xN and BxGa(1-x)N alloys including the systems consisting of low-coordinated atoms.