As a first application of the Schwinger multichannel theory, we have calculated integral and differential cross sections for electron-impact excitation of the transition X 1Σg+→b 3Σu+ in H2 for scattering energies from 13 to 30 eV at the two-state level. We find good agreement between our integral cross sections and the results obtained previously in a two-state close-coupling study. Our method does not rely on single-center expansions to calculate the body-frame scattering amplitude and is designed to be applicable to molecules of arbitrary geometry