Nanoscale variations of optical properties in transition metal dichalcogenide (TMD) monolayers can be explored with cathodoluminescence (CL) and electron energy loss spectroscopy (EELS) using electron microscopes. To increase the CL emission intensity from TMD monolayers, the MoSe2 flakes are encapsulated in hexagonal boron nitride (hBN), creating van der Waals (VdW) heterostructures. Until now, the studies have been exclusively focused on scanning transmission electron microscopy (STEM-CL) or scanning electron microscopy (SEM-CL), separately. Here, we present results, using both techniques on the same sample, thereby exploring a large acceleration voltage range. We correlate the CL measurements with STEM-EELS measurements acquired with different energy dispersions, to access both the low-loss region at ultra-high spectral resolution, and the core-loss region. This provides information about the weight of the various absorption phenomena including the direct TMD absorption, the hBN interband transitions, the hBN bulk plasmon, and the core losses of the atoms present in the heterostructure. The S(T)EM-CL measurements from the TMD monolayer only show emission from the A exciton. Combining the STEM-EELS and S(T)EM-CL measurements, we can reconstruct different decay pathways leading to the A exciton CL emission. The comparison with SEM-CL shows that this is also a good technique for TMD heterostructure characterization, where the reduced demands on sample preparation are appealing. To demonstrate the capabilities of SEM-CL imaging, we also measured on a SiO2/Si substrate, quintessential in the sample preparation of two-dimensional materials, which is electron-opaque and can only be measured in SEM-CL. The CL-emitting defects of SiO2 make this substrate challenging to use, but we demonstrate that this background can be suppressed by using lower electron energy.