  We present theoretical results for the radiative rates and doping-dependent
photoluminescence spectrum of interlayer excitonic complexes localized by donor
impurities in MoSe$_2$/WSe$_2$ twisted heterobilayers, supported by quantum
Monte Carlo calculations of binding energies and wave-function overlap
integrals. For closely aligned layers, radiative decay is made possible by the
momentum spread of the localized complexes' wave functions, resulting in few
$\mu$s$^{-1}$ radiative rates. For strongly misaligned layers, the short-range
interaction between the carriers and impurity provides a finite radiative rate
with a strong asymptotic twist angle dependence $\propto \theta^{-8}$. Finally,
phonon-assisted recombination is considered, with emission of optical phonons
in both layers resulting in additional weaker emission lines, redshifted by the
phonon energy.
