Spatially resolved electron-energy-loss spectroscopy (EELS) is performed at diffuse interfaces between MoS2 and MoSe2 single layers. With a monochromated electron source (20 meV) we successfully probe excitons near the interface by obtaining the low loss spectra at the nanometer scale. The exciton maps clearly show variations even with a 10 nm separation between measurements; consequently, the optical band gap can be measured with nanometer-scale resolution, which is 50 times smaller than the wavelength of the emitted photons. By performing core-loss EELS at the same regions, we observe that variations in the excitonic signature follow the chemical composition. The exciton peaks are observed to be broader at interfaces and heterogeneous regions, possibly due to interface roughness and alloying effects. Moreover, we do not observe shifts of the exciton peak across the interface, possibly because the interface width is not much larger than the exciton Bohr radius.