Recently, a number of new two-dimensional (2D) materials based on puckered phosphorene and arsenene have been predicted with moderate band gaps, good absorption properties and carrier mobilities superior to those of transition metal dichalcogenides. For heterojunction applications, it is important to know the relative band alignment of these new 2D materials. We report the band alignment of puckered CaP₃, CaAs₃ and BaAs₃ monolayers at the quasiparticle level of theory (G₀W₀), calculating band offsets for isolated monolayers according to the electron affinity rule. Our calculations suggest that monolayer CaP₃, CaAs₃ and BaAs₃ all form type-II (staggered) heterojunctions which makes them suitable for solar-energy conversion applications. Their quasiparticle gaps are 2.1 (direct), 1.8 (direct) and 1.5 eV (indirect), respectively. We also examine trends in the electronic structure in the light of chemical bonding analysis. We show that the indirect band gap in monolayer BaAs₃ is caused by relatively strong As 3p–Ba 5d bonding interactions. Our results provide guidance for the design of phosphorene-like materials and their heterojunction applications.