Two quantum dots with tunable mutual tunnel coupling have been embedded in a two-terminal Aharonov-Bohm geometry. Aharonov-Bohm oscillations investigated in the cotunneling regime demonstrate coherent tunneling through nonresonant states. Visibilities of more than 0.8 are measured indicating that phase-coherent processes are involved in the elastic and inelastic cotunneling. An oscillation-phase change of pi is detected as a function of bias voltage at the inelastic cotunneling onset.