We present spectral measurements made in the soft (20–100 keV) γ-ray band of the region containing the composite supernova remnant G11.2-0.3 and its associated pulsar PSR J1811−1925. Analysis of INTEGRAL/IBIS data allows characterization of the system above 10 keV. The IBIS spectrum is best fitted by a power law having photon index Γ= 1.8+0.4−0.3 and a 20–100 keV flux of 1.5 × 10−11 erg cm−2 s−1 . Analysis of archival Chandra data over different energy bands rules out the supernova shell as the site of the soft γ-ray emission while broadband (1–200 keV) spectral analysis strongly indicates that the INTEGRAL/IBIS photons originate in the central zone of the system which contains both the pulsar and its nebula. The composite X-ray and soft γ-ray spectrum indicates that the pulsar provides around half of the emission seen in the soft γ-ray domain; its spectrum is hard with no sign of a cut off up to at least 80 keV. The other half of the emission above 10 keV comes from the pulsar wind nebula; with a Γ= 1.7 its spectrum is softer than that of the pulsar. From the IBIS/ISGRI mosaics we are able to derive 2σ upper limits for the 20–100 keV flux from the location of the nearby TeV source HESS J1809−193 to be 4.8 × 10−12 erg cm−2 s−1 . We have also examined the likelihood of an association between PSR J1811−1925 and HESS J1809−193. Although PSR J1811−1925 is the most energetic pulsar in the region, the only one detected above 10 keV and thus a possible source of energy to fuel the TeV fluxes, there is no morphological evidence to support this pairing, making it an unlikely counterpart.