Speech signals encode emotional, linguistic, and pathological information within a shared acoustic channel; however, disentanglement is typically assessed indirectly through downstream task performance. We introduce an information-theoretic framework to quantify cross-dimension statistical dependence in handcrafted acoustic features by integrating bounded neural mutual information (MI) estimation with non-parametric validation. Across six corpora, cross-dimension MI remains low, with tight estimation bounds ($< 0.15$ nats), indicating weak statistical coupling in the data considered, whereas Source--Filter MI is substantially higher (0.47 nats). Attribution analysis, defined as the proportion of total MI attributable to source versus filter components, reveals source dominance for emotional dimensions (80\%) and filter dominance for linguistic and pathological dimensions (60\% and 58\%, respectively). These findings provide a principled framework for quantifying dimensional independence in speech.

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