For most black hole X-ray binaries, the fraction of X-ray flux originating in the synchrotron jets is generally thought to be low in the hard state. However in one intriguing case, using infrared -X-ray correlations, evolution of broadband spectra and timing signatures we show that synchrotron emission from a jet likely dominated both the infrared and X-ray flux on the hard state decline of an outburst of XTE J1550-564 at a luminosity of ˜ (2 × 10-4 -2 × 10-3 ) LEdd . Synchrotron emission from the relativistic jets launched close to black holes can be highly linearly polarized, depending on the configuration of the magnetic field. We show that the polarimetric signature of their jets is detected in the infrared and is highly variable. This reveals the magnetic geometry in the compact jet, in a region close enough to the black hole that it is influenced by its strong gravity. We also present the first ever test for a correlation between optical polarization and X-ray flux of an X-ray binary, using data taken simultaneously with sub-second time resolution. From these results, we predict that in some cases, high (possibly up to 10%), variable levels of X-ray polarization from synchrotron emission from the jets will be detected from accreting black holes by future spaceborne X-ray polarimeters.