Atoms from an otherwise unconfined 87Rb condensate are shown to be suspended against gravity using repeated reflections from a pulsed optical standing wave. Reflection efficiency was optimized using a triple-pulse sequence that, theoretically, provides accuracies better than 99.9%. Experimentally, up to 100 reflections are observed, leading to dynamical suspension for over 100 ms. The velocity sensitivity of the reflections can be used to determine the local gravitational acceleration. Further, a gravitationally sensitive atom interferometer was implemented using the suspended atoms, with packet coherence maintained for a similar time. These techniques could be useful for the precise measurement of gravity when it is impractical to allow atoms to fall freely over a large distance.