We have measured the photodissociation spectrum of CH(+) and CD(+) molecular ions, stored as fast (MeV) ion beams in the heavy-ion storage ring TSR. Several b (3)Sigma(-)-a (3)Pi bands were observed as strong resonances because a large fraction of the ions in the metastable a (3)Pi(v=0) state were pumped to b (3)Sigma(-) levels and predissociated via the c (3)Sigma(+) state into C(+) and H(D) fragments. From a rotational analysis of the 2-0, 3-0, and 4-0 bands in CH(+) and the 3-0 and 4-0 bands in CD(+), we derive spectroscopic constants for these levels and also revise a previous analysis of the 0-0 and 1-0 bands in CH(+). Combining all data delivers new, significantly adjusted equilibrium constants for the b (3)Sigma(-) and a (3)Pi electronic states. Apart from the spectroscopic analysis, we estimate the predissociation rates of the upper b (3)Sigma(-) vibrational levels in CH(+) and compare them to a model. For the initial rovibrational distribution of the stored metastable CH(+) molecules, the data indicate a faster vibrational cooling than derived before, and rotational cooling at a rate similar to the X (1)Sigma(+) ground state. New aspects of the spin-forbidden a (3)Pi-X (1)Sigma(+) radiative decay are discussed. Finally, we predict b (3)Sigma(-)-a (3)Pi absorption and a (3)Pi-X (1)Sigma(+) emission lines through which CH(+) in the metastable a (3)Pi(v=0) state might be detectable in astrophysical environments.