An electrically conductive metal typically transmits or absorbs a spin current. Here, we report on evidence that interfacing two metal thin films can suppress spin transmission and absorption. We examine spin pumping in spin-source/spacer/spin-sink heterostructures, where the spacer consists of metallic Cu and Cr thin films. The Cu/Cr spacer largely suppresses spin pumping—i.e., neither transmitting nor absorbing a significant amount of spin current—even though Cu or Cr alone transmits a sizable spin current. The antiferromagnetism of Cr is not essential for the suppression of spin pumping, as we observe similar suppression with Cu/V spacers with V as a nonmagnetic analog of Cr. We speculate that diverse combinations of spin-transparent metals may form interfaces that suppress spin pumping, although the underlying mechanism remains unclear. Our work may stimulate a new perspective on spin transport in metallic multilayers.