Causal inference under interventions requires accurate assessment of differences between true and learned causal graphs. We introduce a new continuous metric that extends beyond graph-based measures like Structural Hamming Distance and Structural Intervention Distance by incorporating underlying data alongside graph structures. Our approach embeds intervention distributions for each node pair as conditional mean embeddings in reproducing kernel Hilbert spaces, then quantifies their disparity using maximum (conditional) mean discrepancy. We present theoretical findings supported by synthetic data experiments.