Decaying dark matter (DDM) affects the evolution of cosmic structure relative to standard cold, collisionless, stable dark matter (CDM). We introduce a new semianalytic model for the effects of two-body DDM on halo structure and subhalo populations. In this scenario, cold parent dark matter particles decay into less massive daughter particles plus dark radiation with a lifetime comparable to the age of the Universe. Our DDM model is implemented in the open-source software alacticus and accounts for heating (due to the velocity kicks imparted on daughter particles) and mass loss (due to the parent-daughter mass splitting). We show that decays flatten and reduce the amplitude of halos’ inner density profiles. These effects make DDM subhalos susceptible to tidal disruption, which we show yields a mass-dependent suppression of the subhalo mass function relative to CDM. Our predictions for DDM density profiles, velocity dispersion profiles, and subhalo populations are consistent with results from isolated and cosmological DDM N-body simulations. Thus, our model enables efficient and accurate exploration of DDM parameter space and will be useful for deriving constraints from upcoming small-scale structure observations.