We characterize attosecond transient absorption spectroscopy (ATAS) in molecules with coupled nuclear and electronic dynamics in the vicinity of a conical intersection between adiabatic potential energy surfaces. With respect to ATAS, the nonadiabatic vibronic coupling strength can be divided into weak, intermediate, and strong, and the characteristics of spectra belonging to each of these domains are discussed. The results can guide the analysis of ATAS experiments in molecules with conical intersections.