The transmission behaviour of a distributed Bragg reector (DBR) with surface dielectric gratings on top and bottom is studied. The transmission shows a comb-like spectrum in the DBR band gap, which is explained in the Fano picture. The number density of the transmission peaks increases with increasing number of cells of the DBR, while the ratio of the average full width at half maximum to the corresponding average free spectral range, being only few percent for both transversal electric and magnetic waves, is almost invariant. The transmission peaks can be narrower than 0.1 nm and are fully separated from each other in certain wavebands. We further prove that the transmission combs are robust against randomness in the heights of the DBR layers. Therefore, the proposed structure is a candidate for an ultra-narrow-band multichannel filter or polarizer.