Affective empathy (AE) is distinguished clinically and neurally from cognitive empathy (CE). While AE is selectively disrupted in psychopathy, autism is associated with deficits in CE. Despite such dissociations, AE and CE together contribute to normal human empathic experience. A dimensional measure of individual differences in AE 'relative to' CE captures this interaction and may reveal brain-behavior relationships beyond those detectable with AE and CE separately. Using resting-state fMRI and measures of empathy in healthy adults, we show that relative empathic ability (REA) is reflected in the brain's intrinsic functional dynamics. Dominance of AE was associated with stronger functional connectivity among social-emotional regions (ventral anterior insula, orbitofrontal cortex, amygdala, perigenual anterior cingulate). Dominance of CE was related to stronger connectivity among areas implicated in interoception, autonomic monitoring and social-cognitive processing (brainstem, superior temporal sulcus, ventral anterior insula). These patterns were distinct from those observed with AE and CE separately. Finally, REA and the strength of several functional connections were associated with symptoms of psychopathology. These findings suggest that REA provides a dimensional index of empathic function and pathological tendencies in healthy adults, which are reflected in the intrinsic functional dynamics of neural systems associated with social and emotional cognition.