A detailed study of Higgs interference effects at the one-loop level in the 1-Higgs-Singlet extension of the Standard Model (1HSM) is presented for the W + W − and tt decay modes with fully leptonic W W decay. We explore interference effects for benchmark points with a heavy Higgs mass that significantly exceeds 2m t . In the W W channel, the Higgs signal and the interfering continuum background are loop induced. In the tt channel, which features a tree-level background, we also calculate the interference with the one-loop background, which, due to the appearance of the absorptive part, is found to dominate the normalisation and shape of differential Higgs cross section distributions and should therefore be considered in experimental analyses. The commonly used geometric average K-factor approximation K interference ≈ (K Higgs K background ) 1/2 is not appropriate. We calculate with massive top and bottom quarks. Our 1HSM and SM implementation in Sherpa+OpenLoops is publicly available and can be used as parton-level integrator or event generator.