A coarse-grained, rigid-rod model that includes steric interactions and an internal dipole is used to study monolayers of surfactant molecules tethered to a flat interface. Monte Carlo simulations are performed in the canonical ensemble for a range of high-density configurations with varying degrees of dipole strength. Both a melting transition and a tilting transition are observed, and the dependence of the transitions on the surfactant molecules' internal dipoles is examined. Simulation results indicate that at high packing densities, the monolayers exist in a frustrated state due to dipole-dipole repulsions and steric interactions. Tilting of the surfactant molecules increases the magnitude of the dipole-dipole attractions and lowers the overall system energy, but is limited by steric repulsions. In simulations with higher dipole strengths, the melting and tilting transitions are found to be coupled. The formation of nanodomains with increased collective tilt and positional order in these systems suggests a possible mechanism for the coupling.