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We present a generalization of the variationally stable method of Gao and Starace [B. Gao and A. F. Starace, Phys. Rev. Lett. 61, 404 (1988); Phys. Rev. A 39, 4550 (1989)] for two-electron atoms and ions that incorporates a coupled-channel adiabatic hyperspherical approach. Using this approach, we report results for two-photon detachment of H-, in which we have coupled one, two, three, and four adiabatic hyperspherical channels within each term level of the initial, intermediate, and final states. We present results also for the dynamic polarizability of H- as well as for the one-photon detachment cross section. Comparisons are given with results of prior work.