In this third paper on sulfur species, we have conducted a survey of SO+ (two transitions) and H2S (one transition) in our standard samples of 11 cirrus cores and 27 Clemens-Barvainis translucent objects whose structures and chemistry have been studied earlier in this series. SO+(2II½, J = 3/2-1/2) is seen weakly in 12 objects, while H2S (110 -101) is detected quite strongly in 31 objects. These results are modeled in terms of our previous hydrostatic equilibrium and n ∼r-α structures together with other chemical and physical properties derived earlier. The typical H2S fractional abundance is large, ∼1 × 10-8, and increases monotonically with increasing extinction in the 1.2-2.7 mag range (edge-to-center). Thus H2S displays the same characteristic transition between diffuse and dense cloud chemistry as do SO, SO2, CS, HCS +, HCO +, and other species studied in this series. By contrast, the SO + abundances are small, 1 × 10-9, and exhibit a marginal decrease with increasing extinction. The simple ion-molecule network as used by Turner for sulfur chemistry includes the sulfur hydride species and predicts the observed parameters of SO+ but predicts an H2S abundance 2 orders of magnitude less than observed. Of the 10 species presently analyzed in detail in the translucent cores, H2S is only the second (along with H2CO) that fails to be explained in detail by quiescent cloud ion-molecule chemistry. Various catalytic models of H2S on grains are discussed. Photocatalysis of H2S is found capable of producing the observed abundances but only for sizable accreted mantles. Other types of surface chemistry are also successful but are close to the limits of possible efficiencies.We have detected OCS and H2CS in one object, CB 17, with abundances of 1 × 10-9 and 7 × 10-9 respectively. Our ion-molecule model has been expanded to include OCS and H2CS chemistry. We find that the model fits observed abundances within a factor of 3 for both species.