A millimeter-wave passive-integrated bandstop filter (BSF) with absorptive/reflectionless behavior is reported. It avoids the creation of RF-power reflections for filtered signals which can deteriorate earlier active stages in integrated RF front-end chains. It exploits a two-path transversal configuration in a multi-layer structure. Specifically, it is composed of a direct transmission line for the main path (top layer) and two lossy edge-grounded spiral-shaped resonators for the secondary path (bottom layer) that are coupled between them and to the main path. Thus, a sharp second-order stopband is created through destructive signal-interference effects between the two signal paths with intrinsic RF-power absorption within the volume of the lossy resonators. As practical validation, a 24.5-GHz on-chip millimeter-wave absorptive BSF circuit is built in a 0.13-<inline-formula> <tex-math notation="LaTeX">\mu \text{m} </tex-math></inline-formula> SiGe bipolar complementary metal-oxide-semiconductor (Bi)-CMOS technology and tested. Close agreement between simulated and measured results for this on-chip BSF circuit is achieved.