Ultrashort laser pulses have thus far been used in two distinct modes. In the time domain, the pulses have allowed probing and manipulation of dynamics on a subpicosecond time scale. More recently, phase stabilization has produced optical frequency combs with absolute frequency reference across a broad bandwidth. Here we combine these two applications in a spectroscopic study of rubidium atoms. A wide-bandwidth, phase-stabilized femtosecond laser is used to monitor the real-time dynamic evolution of population transfer. Coherent pulse accumulation and quantum interference effects are observed and well modeled by theory. At the same time, the narrow linewidth of individual comb lines permits a precise and efficient determination of the global energy-level structure, providing a direct connection among the optical, terahertz, and radio-frequency domains. The mechanical action of the optical frequency comb on the atomic sample is explored and controlled, leading to precision spectroscopy with an appreciable reduction in systematic errors.