We present the results of our observations of the early stages of the 2012–2013 outburst of the transient black hole X-ray binary ( BHXRB ) , Swift J1745 - 26 , with the VLA , SMA , and JCMT ( SCUBA–2 ) . Our data mark the first multiple-band mm & sub-mm observations of a BHXRB . During our observations the system was in the hard accretion state producing a steady , compact jet . The unique combination of radio and mm/sub-mm data allows us to directly measure the spectral indices in and between the radio and mm/sub-mm regimes , including the first mm/sub-mm spectral index measured for a BHXRB . Spectral fitting revealed that both the mm ( 230 GHz ) and sub-mm ( 350 GHz ) measurements are consistent with extrapolations of an inverted power-law from contemporaneous radio data ( 1–30 GHz ) . This indicates that , as standard jet models predict , a power-law extending up to mm/sub-mm frequencies can adequately describe the spectrum , and suggests that the mechanism driving spectral inversion could be responsible for the high mm/sub-mm fluxes ( compared to radio fluxes ) observed in outbursting BHXRBs . While this power-law is also consistent with contemporaneous optical data , the optical data could arise from either jet emission with a jet spectral break frequency of \nu _ { { break } } \gtrsim 1 \times 10 ^ { 14 } { Hz } or the combination of jet emission with a lower jet spectral break frequency of \nu _ { { break } } \gtrsim 2 \times 10 ^ { 11 } { Hz } and accretion disc emission . Our analysis solidifies the importance of the mm/sub-mm regime in bridging the crucial gap between radio and IR frequencies in the jet spectrum , and justifies the need to explore this regime further .