A number of central nervous system (CNS) diseases exhibit changes in myelin content and magnetic resonance longitudinal, T1, and transverse, T2, relaxation times, which therefore represent important biomarkers of CNS pathology. Among the methods applied for measurement of myelin water fraction (MWF) and relaxation times, the multicomponent driven equilibrium single pulse observation of T1 and T2 (mcDESPOT) approach is of particular interest. mcDESPOT permits whole brain mapping of multicomponent T1 and T2, with data acquisition accomplished within a clinically realistic acquisition time. Unfortunately, previous studies have indicated the limited performance of mcDESPOT in the setting of the modest signal-to-noise range of high-resolution mapping, required for the depiction of small structures and to reduce partial volume effects. Recently, we showed that a new Bayesian Monte Carlo (BMC) analysis substantially improved determination of MWF from mcDESPOT imaging data. However, our previous study was limited in that it did not discuss determination of relaxation times. Here, we extend the BMC analysis to the simultaneous determination of whole-brain MWF and relaxation times using the two-component mcDESPOT signal model. Simulation analyses and in-vivo human brain studies indicate the overall greater performance of this approach compared to the stochastic region contraction (SRC) algorithm, conventionally used to derive parameter estimates from mcDESPOT data. SRC estimates of the transverse relaxation time of the long T2 fraction, T2,l, and the longitudinal relaxation time of the short T1 fraction, T1,s, clustered towards the lower and upper parameter search space limits, respectively, indicating failure of the fitting procedure. We demonstrate that this effect is absent in the BMC analysis. Our results also showed improved parameter estimation for BMC as compared to SRC for high-resolution mapping. Overall we find that the combination of BMC analysis and mcDESPOT, BMC-mcDESPOT, shows excellent performance for accurate high-resolution whole-brain mapping of MWF and bi-component transverse and longitudinal relaxation times within a clinically realistic acquisition time.