Surface-based cortical registration methods that are driven by geometrical features, such as folding, provide sub-optimal alignment of many functional areas due to variable correlation between cortical folding patterns and function. This has led to the proposal of new registration methods using features derived from functional and diffusion imaging. However, as yet there is no consensus over the best set of features for optimal alignment of brain function. In this paper we demonstrate the utility of a new Multimodal Surface Matching (MSM) algorithm capable of driving alignment using a wide variety of descriptors of brain architecture, function and connectivity. The versatility of the framework originates from adapting the discrete Markov Random Field (MRF) registration method to surface alignment. This has the benefit of being unconstrained by choice of a similarity measure and relatively insensitive to local minima. The method offers significant flexibility in the choice of feature set, and we demonstrate the advantages of this by performing registrations using univariate descriptors of surface curvature and myelination, multivariate feature sets derived from resting fMRI, and multimodal descriptors of surface curvature and myelination. We compare the results with two state of the art surface registration methods that use geometric features: FreeSurfer and Spherical Demons. In the future, the MSM technique will allow explorations into the best combinations of features and alignment strategies for inter-subject alignment of cortical functional areas for a wide range of neuroimaging data sets.