The aim of this paper is to report on the results of a multicolour observing campaign performed at the LBT on the interstellar comet 2I/Borisov during three epochs while target was approaching its perihelion: UBVRI images have been observed in October and December 2019, when the comet was at ∼2.3 and 2.0 au from the Sun, respectively. Comet Borisov presented a rather complex morphology, especially in the December observing epoch, when a bi-lobate structure on a global scale was visible, with a jet-like structure characterised by a disconnection event, probably due to the presence of an active area on the nucleus' surface combined with its rotational properties. U - B colour, measured for the first time for this comet, monotonically decreases as Borisov approaches perihelion, from 0.35 ± 0.05 in October 19th to -0.07 ± 0.05 in December 2nd; B - V colour shows a more chaotic behaviour, with values for October epochs quite similar to solar colours, and a higher value of 0.76 ± 0.04 in December 2nd, probably due to a combination of an increase of the B flux (CN emission) and of an increase in V flux (due to C2). V - R and R-I colours derived in both the October and December observing epochs depict a scenario of a coma slightly redder than the Sun, with a RI-reddening value of ∼11%/1000 Å and ∼5%/1000 Å, respectively. The R- Afρ at the reference aperture of r ∼104 km from the optocentre slightly decreases from ∼100 cm (October) to ∼ 70 cm (December), showing that the Borisov's dust environment is quite similar to those of Short Period Comets of our Solar System. The application of a first-order photometric model, with the plausible scenario of grains with radius a = 100 μm and bulk density ρd = 1000 kg/m3 moving at vd in the range of 3-30 m/s, allows to derive a dust production rate Qd decrease from a range of 3-25 kg/s in October to a range of 2-18 kg/s in December.All these results confirm that the interstellar comet 2I/Borisov has a coma environment quite similar to that of the Short Period Comets (mostly Jupiter Family targets) orbiting in our inner Solar System.