  Understanding the properties of the galactic emission at millimetre
wavelengths is important for studies of the cosmic microwave background (CMB).
In this work we explore the bispectrum, the harmonic equivalent of the three
point function, from galactic dust and synchrotron emission. We investigate
these effects across a broad range of frequencies using the synchrotron
dominated S-band Polarization All Sky Survey (SPASS) maps at 2.3 GHz, the
Planck satellite maps (30-857 GHz) and dust dominated Infrared Astronomical
Satellite (IRAS) maps at 3 THz. We measure bispectra of total intensity fields,
T, as well as the gradient, E, and curl modes, B, of the polarization field. We
find that the synchrotron and galactic dust have strong temperature bispectra
with significant contributions in the squeezed limit, which probes the
correlations between two small scale modes with a large scale mode.
Additionally, we find that the dust also has strong polarised bispectra that
also peak in the squeezed configuration. We explore parity odd bispectra, such
as BTT bispectra, and find strong parity odd bispectra for the galactic dust
notably in BTT, BTE and BEE configurations. After masking bright sources, we
find no evidence for polarised synchrotron bispectra and no evidence for cross
bispectra between the dust and synchrotron emission. The strong foreground
bispectra discussed here need to be carefully controlled to avoid biasing
measurements of primordial non-Gaussianity. Finally we use these bispectra
tools to test for residual foregrounds in the component separated Planck maps
and find no evidence of residual foregrounds. These tools will be useful for
characterizing residual foregrounds in component separated maps, particularly
for experiments with less frequency coverage than the Planck satellite.
