Quantitative MRI (qMRI) probes the microstructural properties of the central nervous system (CNS) by providing biophysical measures of tissue characteristics. In this work, we aimed to (i) identify qMRI measures that distinguish histological lesion types in postmortem multiple sclerosis (MS) brains, especially the remyelinated ones; and to (ii) investigate the relationship between those measures and quantitative histological markers of myelin, axons, and astrocytes in the same experimental setting. Three fixed MS whole brains were imaged with qMRI at 3T to obtain magnetization transfer ratio (MTR), myelin water fraction (MWF), quantitative T1 (qT1), quantitative susceptibility mapping (QSM), fractional anisotropy (FA) and radial diffusivity (RD) maps. The identification of lesion types (active, inactive, chronic active, or remyelinated) and quantification of tissue components were performed using histological staining methods as well as immunohistochemistry and immunofluorescence. Pairwise logistic and LASSO regression models were used to identify the best qMRI discriminators of lesion types. The association between qMRI and quantitative histological measures was performed using Spearman's correlations and linear mixed-effect models. We identified a total of 65 lesions. MTR and MWF best predicted the chance of a lesion to be remyelinated, whereas RD and QSM were useful in the discrimination of active lesions. The measurement of microstructural properties through qMRI did not show any difference between chronic active and inactive lesions. MWF and RD were associated with myelin content in both lesions and normal-appearing white matter (NAWM), FA was the measure most associated with axon content in both locations, while MWF was associated with astrocyte immunoreactivity only in lesions. Moreover, we provided evidence of extensive astrogliosis in remyelinated lesions. Our study provides new information on the discriminative power of qMRI in differentiating MS lesions -especially remyelinated ones- as well as on the relative association between multiple qMRI measures and myelin, axon and astrocytes.