Endogenous brain rhythms occurring at various frequencies and associated with distinct behavioral states provide multiscale temporal windows that enable cells to time their spiking activity with high precision, which is thought to be important for the coding of information in neuronal circuits. However, although the selective timing of GABAergic inputs to specific spatial domains of principal cells are known to play key roles in network oscillations, the in vivo firing patterns of distinct hippocampal interneurons in awake animals are not known. Here we used a combination of juxtacellular labeling techniques with recordings from anesthesia-free, head-fixed mice running or resting on a spherical treadmill to study the oscillation-dependent discharges by two major interneuronal subtypes, the perisomatically projecting parvalbumin-positive basket cells (PVBCs) and distal dendritically projecting oriens lacunosum moleculare (OLM) cells. Recordings of the spiking activity of post hoc-identified CA1 interneurons during theta (5-10 Hz), gamma (25-90Hz), epsilon ("high-gamma"; 90-130 Hz), and ripple (130-200 Hz) oscillations revealed both cell type- and behavioral state-dependent entrainments of PVBC and OLM cell discharges in awake mice. Our results in awake mice differed in several respects from previous data on interneuronal discharge patterns in anesthetized animals. In addition, our results demonstrate a form of frequency-invariant, cell type-specific temporal ordering of inhibitory inputs in which PVBC-derived perisomatic inhibition is followed by OLM cell-generated distal dendritic inhibition during each of the network oscillation bands studied, spanning more than an order of magnitude in frequencies.