We analyse FORS2/VLT $I$-band imaging data to monitor the motions of both components in the nearest known binary brown dwarf WISE J104915.57-531906.1AB (LUH16) over one year. The astrometry is dominated by parallax and proper motion, but with a precision of $sim$0.2 milli-arcsecond per epoch we accurately measure the relative position change caused by the orbital motion of the pair. This allows us to directly measure a mass ratio of $q=0.78pm0.10$ for this system. We also search for the signature of a planetary-mass companion around either of the A and B component and exclude at 3-$sigma$ the presence of planets with masses larger than $2,M_mathrm{Jup}$ and orbital periods of 20--300 d. We update the parallax of LUH16 to $500.51pm0.11$ mas, i.e. just within 2 pc. This study yields the first direct constraint on the mass ratio of LUH16 and shows that the system does not harbour any close-in giant planets.
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