The near-ubiquity of the involvement of RNA in crucial biological processes is accepted. It is important, therefore, to study and understand the biophysical principles that regulate the function of RNA and its interactions with other molecules (e.g., proteins and antibiotics). Methods enabling the high-throughput determination of RNA-protein binding kinetics and thermodynamics would greatly accelerate understanding of these interactions. To that end, we describe the development of a real-time biomolecular interaction analysis platform based on arrayed imaging reflectometry (AIR) for multiplex analysis of RNA-protein interactions. We demonstrate the use of aqueous AIR by measuring the binding kinetics between muscleblind-like 1 (MBNL1), a splicing regulator protein that plays a pivotal role in the Myotonic Dystrophies and Huntington's Disease, and several of its RNA targets simultaneously on a microarrayed chip. Using this approach, we observe that the kinetics of MBNL1 binding isolated CUG and repeat CUG RNA sequences (as models for "normal" and "pathogenic" RNA, respectively) are different even though their steady state binding constants are similar. The ability to compare binding kinetics between RNA sequences rapidly and easily may provide insight into the molecular basis of MBNL1-RNA binding, and more generally suggests that AIR can be a powerful tool to enable the label-free, real-time analysis of biomolecular interactions in a high-throughput format.