The resonance-continuum interference is usually neglected when the width of a resonance is small compared to the resonance mass. We re-examine this standard by studying the interference effects in high-resolution decay channels, \gamma\gamma and ZZ, of the heavy Higgs boson H^0 in nearly aligned two-Higgs-doublet models. For the H^0 with a sub-percent width-to-mass ratio, we find that, in the parameter space where the LHC 14 TeV ZZ resonance search can be sensitive, the interference effects can modify the ZZ signal rate by {\cal O}(10)\% and the exclusion reach by {\cal O}(10) GeV. In other parameter space where the ZZ or \gamma\gamma signal rate is smaller, the LHC 14 TeV reach is absent, but a resonance shape can be much more dramatically changed. In particular, the \gamma\gamma signal rate can change by {\cal O}(100)\%. Relevant to such parameter space, we suggest variables that can characterize a general resonance shape. We also illustrate the relevance of the width on the interference by adding non-standard decay modes of the heavy Higgs boson. Show Partial Abstract