In this work, the theoretical study of the interaction of terahertz (THz) waves with graphene embedded into two different semi-infinite metamaterials was carried out. To model the graphene, the effective surface conductivity approach based on the Kubo formalism was used. In addition, two types of metamaterials, i.e., double-positive (DPS) and double-negative (DNG), were studied in the THz regime. The numerical modeling of metamaterials was performed in the framework of causality-principle-based Kramers-Kronig relations. The reflectance and transmittance from the graphene-embedded metamaterial structures are studied for the following four different configurations: DPS-Graphene-DPS, DPS-Graphene-DNG, DNG-Graphene-DPS, and DNG-Graphene-DNG. The influence of the chemical potential and scattering rate on the reflectance and transmittance for each configuration is analyzed. It is concluded that the DPS-Graphene-DPS and DNG-Graphene-DNG configurations behave as anti-reflectors for the THz waves, while the DPS-Graphene-DNG and DNG-Graphene-DPS configurations are suitable for THz reflector applications. Moreover, a parametric study revealed that the relative permittivity of the partnering metamaterial can be used as an additional degree of freedom to control the reflectance and transmittance of THz waves. In conclusion, the transmissive and reflective characteristics of THz waves can be controlled effectively with the appropriate choice of graphene parameters, as well as the configuration of metamaterial structures. The convergence of the analytical and numerical results is found with the published results under special conditions. The present work may have potential applications in the design of THz wave controllers, reflectors, absorbers, and anti-reflectors.