Van der Waals heterostructures (vdW HTSs) incorporating graphene (GE) have been an active area of research, both theoretical and experimental, due to their potential to yield devices with a wide variety of applications. In this paper, first-principles calculations are employed to investigate C₆N₆/GE, hg-C₃N₄/GE, and C₆N₆/hg-C₃N₄ 2D vdW HTSs. A systematic analysis of structural and thermodynamic stability, electronic, mechanical, and optical properties of semiconductor/metal and semiconductor/semiconductor interfaces is performed. Both semiconductor/metal HTSs form n-type Schottky contacts, which can be converted into p-type Schottky or Ohmic contacts by tuning the external perpendicular electric field and the interlayer coupling. In the semiconductor/semiconductor C₆N₆/hg-C₃N₄ HTS, the valence and conduction band edges originate from distinct layers, resulting in a type-II band alignment that promotes efficient electron-hole (e-h) separation. Furthermore, the band alignment can be effectively tuned between type-I and type-II by applying an external electric field and varying the interlayer distance. From the optical absorption spectra of the HTSs, we concluded that the C₆N₆/GE and hg-C₃N₄/GE exhibit an optical response across a wide frequency range, whereas the C₆N₆/hg-C₃N₄ HTS shows prominent activity primarily in the ultraviolet region. Using the G₀W₀+BSE approach, the exciton binding energies are also calculated for the gapped systems, namely C₆N₆, hg-C₃N₄ monolayers, and their HTS (C₆N₆/hg-C₃N₄), yielding values of 1.01 eV, 1.14 eV, and 1.18 eV, respectively, highlighting strong e-h interactions. Moreover, the band-edge analysis of C₆N₆/hg-C₃N₄ HTS further favors pronounced interlayer e-h coupling.