First-principles calculations are used to explore the geometry, bonding, and electronic properties of MoS2/Ti2C and MoS2/Ti2CY2 (Y = F and OH) semiconductor/metal contacts. The structure of the interfaces is determined. Strong chemical bonds formed at the MoS2/Ti2C interface result in additional states next to the Fermi level, which extend over the three atomic layers of MoS2 and induce a metallic character. The interaction in MoS2/Ti2CY2, on the other hand, is weak and not sensitive to the specific geometry, and the semiconducting nature thus is preserved. The energy level alignment implies weak and strong n-type doping of MoS2 in MoS2/Ti2CF2 and MoS2/Ti2C(OH)2, respectively. The corresponding n-type Schottky barrier heights are 0.85 and 0.26 eV. We show that the MoS2/Ti2CF2 interface is close to the Schottky limit. At the MoS2/Ti2C(OH)2 interface, we find that a strong dipole due to charge rearrangement induces the Schottky barrier. The present interfaces are well suited for application in all-two-dimensional devices.