We consider temporally integrating interferometric measurements and their relation to the coherence properties of nonstationary light. We find that performing such experiments as a function of time delay is equivalent to spectrally resolving the interference patterns, and time-domain coherence information can be obtained from field autocorrelation only if the source is of the Schell-model type. In an analogy to autocorrelation, we introduce field cross-correlation, which can be used to determine the complete complex field of unknown signal pulses if suitable probe pulses are available. We demonstrate our findings with simulated supercontinuum and free-electron laser ensembles, and discuss the prospect of carrying out experiments.