Widespread white matter abnormalities have been reported in schizophrenia, a disorder frequently characterised as a dysconnection syndrome. White matter connectivity in schizophrenia has been predominantly investigated using diffusion weighted imaging, with reductions in fractional anisotropy throughout the brain often interpreted as an indicator of abnormal myelination. However, diffusion weighted imaging lacks specificity and as such a number of microstructural factors besides myelin may be contributing to these results. We utilised multicomponent driven equilibrium single pulse observation of T1 and T2 (mcDESPOT) in medicated patients with chronic schizophrenia, stratified by treatment response status, and healthy controls, in order to assess myelin water fraction (MWF) in these groups. In addition, we assessed cognitive control using the Stroop task to investigate how response inhibition relates to myelination in patients and controls. Both treatment resistant (n = 22) and treatment responsive (n = 21) patients showed reduced MWF compared to healthy controls (n = 24) in bilateral fronto-occipital fasciculi, particularly evident in the vicinity of the striatum und extending to the cerebellum, with no difference between patient groups. Patients showed greater reaction time interference on the Stroop task compared to healthy controls, with no difference between patient groups. Stroop interference was significantly negatively correlated with MWF in the corpus callosum across groups, and MWF differences in this region mediated the behavioural group effects on the Stroop task. These findings support the suitability of mcDESPOT as a myelin-specific measure of abnormal connectivity in schizophrenia, and suggest that treatment resistant schizophrenia is not characterised by more severe abnormalities in myelination or cognitive control compared to treatment responsive schizophrenia.