  Previous analyses of Doppler and Kepler data have found that Sun-like stars
hosting "cold Jupiters" (giant planets with $a\gtrsim 1\,\mathrm{AU}$) almost
always host "inner super-Earths" (1-$4\,R_\oplus$, $a\lesssim1\,\mathrm{AU}$).
Here, we attempt to determine the degree of alignment between the orbital
planes of the cold Jupiters and the inner super-Earths. The key observational
input is the fraction of Kepler stars with transiting super-Earths that also
have transiting cold Jupiters. This fraction depends on both the probability
for cold Jupiters to occur in such systems, and on the mutual orbital
inclinations. Since the probability of occurrence has already been measured in
Doppler surveys, we can use the data to constrain the dispersion of the mutual
inclination distribution. We find $\sigma=11.8^{+12.7}_{-5.5}\,\mathrm{deg}$
(68% confidence) and $\sigma>3.5\,\mathrm{deg}$ (95% confidence), where
$\sigma$ is the scale parameter of the Rayleigh distribution. This suggests
that planetary orbits in systems with cold Jupiters tend to be coplanar -
although not quite as coplanar as those in the Solar System, which have a mean
inclination from the invariable plane of $1.8\,\mathrm{deg}$. We also find
evidence that cold Jupiters have lower mutual inclinations relative to inner
systems with higher transit multiplicity. This suggests a link between the
dynamical excitation in the inner and outer systems. For example, perturbations
from misaligned cold Jupiters may dynamically heat or destabilize systems of
inner super-Earths.
