Catalyzes the hydrolysis of S-inosyl-L-homocysteine (SIH) to L-homocysteine (Hcy) and inosine. Likely functions in a S-adenosyl-L-methionine (SAM) recycling pathway from S-adenosyl-L-homocysteine (SAH) produced from SAM-dependent methylation reactions. Can also catalyze the reverse reaction in vitro, i.e. the synthesis of SIH from Hcy and inosine. H2O + S-inosyl-L-homocysteine = inosine + L-homocysteine Binds 1 NAD(+) per subunit. Amino-acid biosynthesis; S-adenosyl-L-methionine biosynthesis. SAH is a product of SAM methyltransferases and is known to be a feedback inhibitor of these enzymes. As a result of this inhibition, organisms have evolved efficient enzymes to metabolize SAH via different pathways. The pathway found in methanogens differs from the canonical pathway, it uses the deamination of S-adenosyl-L-homocysteine to form S-inosyl-L-homocysteine for the regeneration of SAM from S-adenosyl-L-homocysteine. Belongs to the adenosylhomocysteinase family.