Laughter and speech-laughs are pervasive phenomena found in conversational speech. Nevertheless, few previous studies have compared their acoustic realization to speech. We investigated in this work the suprasegmental characteristics of these two phenomena in relation to speech, by means of a modulation spectrum analysis. Two types of modulation spectra, one encoding the variation of the envelope of the signal and the other one its temporal fine structure, were considered. Using a corpus of spontaneous dyadic interactions, we computed the modulation index spectrum and the f0 spectrum of the three classes of vocalizations considered and we fitted separate generalized additive mixed models for them. The results obtained for the former modulation showed a clear separation between speech, on the one hand, and laughter and speech-laugh, on the other hand, while the f0 spectrum was able to discriminate between all three classes. We conclude with a discussion of the importance of these findings and their implication for laughter detection.