  We investigate how the dark energy properties impact the constraints on the
total neutrino mass in interacting dark energy (IDE) models. In this study, we
focus on two typical interacting dynamical dark energy models, i.e., the
interacting $w$ cold dark matter (I$w$CDM) model and the interacting
holographic dark energy (IHDE) model. To avoid the large-scale instability
problem in IDE models, we apply the parameterized post-Friedmann approach to
calculate the perturbation of dark energy. We employ the Planck 2015 cosmic
microwave background temperature and polarization data, combined with
low-redshift measurements on baryon acoustic oscillation distance scales, type
Ia supernovae, and the Hubble constant, to constrain the cosmological
parameters. We find that the dark energy properties could influence the
constraint limits on the total neutrino mass. Once dynamical dark energy is
considered in the IDE models, the upper bounds of $\sum m_\nu$ will be changed.
By considering the values of $\chi^2_{\rm min}$, we find that in these IDE
models the normal hierarchy case is slightly preferred over the inverted
hierarchy case; for example, $\Delta\chi^2=2.720$ is given in the IHDE+$\sum
m_\nu$ model. In addition, we also find that in the I$w$CDM+$\sum m_\nu$ model
$\beta=0$ is consistent with current observational data inside the 1$\sigma$
range, and in the IHDE+$\sum m_\nu$ model $\beta>0$ is favored at more than
2$\sigma$ level.
