  We study the large-scale clustering of galaxies in the overlap region of the
Baryon Oscillation Spectroscopic Survey (BOSS) CMASS sample and the WiggleZ
Dark Energy Survey. We calculate the auto-correlation and cross-correlation
functions in the overlap region of the two datasets and detect a Baryon
Acoustic Oscillation (BAO) signal in each of them. The BAO measurement from the
cross-correlation function represents the first such detection between two
different galaxy surveys. After applying density-field reconstruction we report
distance-scale measurements $D_V r_s^{\rm fid} / r_s = (1970 \pm 47, 2132 \pm
67, 2100 \pm 200)$ Mpc from CMASS, the cross-correlation and WiggleZ,
respectively. We use correlated mock realizations to calculate the covariance
between the three BAO constraints. The distance scales derived from the two
datasets are consistent, and are also robust against switching the displacement
fields used for reconstruction between the two surveys. This approach can be
used to construct a correlation matrix, permitting for the first time a
rigorous combination of WiggleZ and CMASS BAO measurements. Using a
volume-scaling technique, our result can also be used to combine WiggleZ and
future CMASS DR12 results. Finally, we use the cross-correlation function
measurements to show that the relative velocity effect, a possible source of
systematic uncertainty for the BAO technique, is consistent with zero for our
samples.
