For the first time, we investigate the X-ray/infrared (IR) correlation for star-forming galaxies at z~1, using SPIRE submm data from the recently-launched Herschel Space Observatory and deep X-ray data from the 2Ms Chandra deep field north (CDFN) survey. We examine the X-ray/IR correlation in the soft X-ray (SX, 0.5-2 keV) and hard X-ray (HX, 2-10 keV) bands by comparing our z~1 SPIRE-detected star-forming galaxies (SFGs) to equivalently IR-luminous (L_IR >10^10 L_sun) samples in the local/low redshift Universe. Our results suggest that the X-ray/IR properties of the SPIRE SFGs are on average similar to those of their local counterparts, as we find no evidence for evolution in the L_SX/L_IR and L_HX/L_IR ratios with redshift. We note however, that at all redshifts, both L_SX/L_IR and L_HX/L_IR are strongly dependent on IR luminosity, with luminous and ultraluminous infrared galaxies (LIRGs and ULIRGs,L_IR >10^11 L_sun) having up to an order of magnitude lower values than normal infrared galaxies (L_IR <10^11 L_sun). We derive a L_SX-L_IR relation and confirm the applicability of an existing L_HX-L_IR relation for both local and distant LIRGs and ULIRGs, consistent with a scenario where X-ray luminosity is correlated with the star-formation rate (SFR).