Context : The Magellanic Clouds provide a nearby laboratory for metal-poor dwarf galaxies . The low dust abundance enhances the penetration of UV photons into the interstellar medium ( ISM ) , resulting in a relatively larger filling factor of the ionized gas . Furthermore , there is very likely a molecular gas reservoir probed by the [ C ii ] 157 \mu m line not traced by CO ( 1-0 ) , the so-called “ dark ” gas . The Herschel Space Telescope allows us to observe far-infrared ( FIR ) cooling lines and to examine the physical conditions in the gas phases of a low-metallicity environment to unprecedented , small spatial scales . Aims : Our objective is to interpret the origin of the diffuse emission of FIR cooling lines in the H ii  region N 11B in the Large Magellanic Cloud . We first investigate the filling factor of the ionized gas . We then constrain the origin of the [ C ii ] line by comparing to tracers of the low-excitation ionized gas and of photodissociation regions ( PDRs ) . Methods : We present Herschel /PACS maps of N 11B in several tracers , [ C ii ] 157 \mu m , [ O i ] 63 \mu m and 145 \mu m , [ N ii ] 122 \mu m , [ N iii ] 57 \mu m , and [ O iii ] 88 \mu m. Optical images in H \alpha and [ O iii ] 5007à  were used as complementary data to investigate the effect of dust extinction . Observations were interpreted with photoionization models to infer the gas conditions and estimate the ionized gas contribution to the [ C ii ] emission . PDRs were probed through polycyclic aromatic hydrocarbons ( PAHs ) observed with the Spitzer Space Telescope . Results : [ O iii ] 88 \mu m is dominated by extended emission from the high-excitation diffuse ionized gas . This is the brightest FIR line throughout N 11B , \sim 4 times brighter than [ C ii ] . We find that about half of the emission from the ionized gas is extinguished by dust . We modeled [ O iii ] around each O-type star and find that the density of the ISM is \lesssim 16 cm ^ { -3 }  on large scales . The extent of the [ O iii ] emission suggests that the medium is rather fragmented , allowing far-UV photons to permeates the ISM to scales of \gtrsim 30 pc . Furthermore , by comparing [ C ii ] with [ N ii ] 122 \mu m , we find that 95 %  of [ C ii ] arises in PDRs , except toward the stellar cluster for which as much as 15 %  could arise in the ionized gas . We find a remarkable correlation between [ C ii ] + [ O i ] and PAH emission , with [ C ii ] dominating the cooling in diffuse PDRs and [ O i ] dominating in the densest PDRs . The combination of [ C ii ] and [ O i ] provides a proxy for the total gas cooling . Our results suggest that PAH emission describes better the gas heating in PDRs as compared to the total infrared emission . Conclusions :