Soft x-ray reflection and transmission spectra of radiation propagating inside microchannel plates have been analyzed in the framework of the wave approximation. X-ray and fluorescence yields due to the grazing incidence reflection phenomenon have been investigated with respect to the geometry of the channel walls. We also discuss x-ray absorption near-edge structure spectra collected at the exit of microcapillaries under the total x-ray reflection condition, taking into account a surface transition layer at the sample surface. The fine structures and the angular distribution of the transmitted radiation have been interpreted in the energy range of the anomalous dispersion of the Si L2,3 edges.