Jahn-Teller coupling effects in doubly degenerate Rydberg series (np(x,y) and nd(xz,yz,) respectively) converging towards the doubly degenerate X approximately 2E1g ion core of benzene are analyzed in a multichannel quantum-defect description. The model includes Jahn-Teller coupling (via the lowest-frequency E2g mode nu-6) in the ion core and in the Rydberg orbitals, as well as the interaction of degenerate electronic channels. Fast internal-conversion processes in the Rydberg manifold of benzene are included in a phenomenological manner via an absorptive imaginary part of the reactance matrix. The model parameters are determined from the analysis of existing multiphoton absorption spectra of low Rydberg members. Absorption spectra of the complete np(x,y) and nd(xz,yz) series and near-threshold photoionization cross sections are calculated, including hot-band spectra (one quantum of nu-6 excited in the initial electronic state). The results are of relevance for the assignment of the enigmatic vibronic structure of the 3p1A2u and 3p1E2u Rydberg states and for the understanding of autoionization dynamics in benzene.