Natural stimulus functional magnetic resonance imaging (N-fMRI) such as fMRI acquired when participants were watching video streams or listening to audio streams has been increasingly used to investigate functional mechanisms of the human brain in recent years. One of the fundamental challenges in functional brain mapping based on N-fMRI is to model the brain's functional responses to continuous, naturalistic and dynamic natural stimuli. To address this challenge, in this paper we present a data-driven approach to exploring functional interactions in the human brain during free listening to music and speech streams. Specifically, we model the brain responses using N-fMRI by measuring the functional interactions on large-scale brain networks with intrinsically established structural correspondence, and perform music and speech classification tasks to guide the systematic identification of consistent and discriminative functional interactions when multiple subjects were listening music and speech in multiple categories. The underlying premise is that the functional interactions derived from N-fMRI data of multiple subjects should exhibit both consistency and discriminability. Our experimental results show that a variety of brain systems including attention, memory, auditory/language, emotion, and action networks are among the most relevant brain systems involved in classic music, pop music and speech differentiation. Our study provides an alternative approach to investigating the human brain's mechanism in comprehension of complex natural music and speech.