Atomic three-level A systems dressed by two coherent electromagnetic fields can exhibit coherent population trapping and electromagnetically induced transparency (EIT) due to quantum interference. By addressing the combined qubit-cavity states of a superconducting transmon qubit in a three-dimensional copper cavity with two microwave drives we establish an effective A system, two legs of which are defined by a dipole transition and a two-photon transition. This circuit-based system allows the observation of three-microwave-photon Raman coherence effects, including coherent population trapping and EIT, which are demonstrated here with both steady-state spectroscopic techniques and time-domain measurements. By sending Gaussian microwave pulses through the cavity in the EIT regime, a negative group velocity of the pulse is observed with the peak of the pulse exiting the cavity 9.4 mu s before entering.