  We present a new model for the cross-covariance between galaxy redshift-space
distortions and peculiar velocities. We combine this with the auto-covariance
models of both probes in a fully self-consistent, maximum-likelihood method,
allowing us to extract enhanced cosmological parameter constraints. When
applying our method to the 6-degree Field Galaxy Survey (6dFGS), our constraint
on the growth rate of structure is $f\sigma_8 = 0.384 \pm 0.052 \rm{(stat)} \pm
0.061 \rm{(sys)}$ and our constraint for the redshift-space distortion
parameter is $\beta = 0.289^{+0.044}_{-0.043} \rm{(stat)} \pm 0.049
\rm{(sys)}$. We find that the statistical uncertainty for the growth rate of
structure is reduced by 64% when using the complete covariance model compared
to the redshift-space distortion auto-covariance model and 50% when compared to
using the peculiar velocity auto-covariance model. Our constraints are
consistent with those from the literature on combining multiple tracers of
large-scale structure, as well as those from other 6dFGS analyses. Our
measurement is also consistent with the standard cosmological model.
