Based on first-principles calculations, the materials properties (structural, electronic, vibrational, and optical properties) of out-of-plane heterostructures formed from the transition metal dichalcogenides, specifically MoS₂-WSe₂ and WS₂-MoSe₂, were investigated. The heterostructures of MoS₂-WSe₂ and WS₂-MoSe₂ are found to be direct and indirect band gap semiconductors, respectively. However, a direct band gap in the WS₂-MoSe₂ heterostructure can be achieved by applying compressive strain. Furthermore, the excitonic peaks in both monolayer and bilayer heterostructures are calculated to understand the optical behavior of these systems. The suppression of the optical spectrum with respect to the corresponding monolayers is due to interlayer charge transfer. The stability of the systems under study is confirmed by performing phonon spectrum calculations.