  We present a measurement of the decay amplitudes in B-->J/psi K^*(892)
channels using 20.7 fb-1 of data collected at the Upsilon(4S) resonance with
the BABAR detector at PEP-II. We measure a P-wave fraction R_perp =
(16.0+/-3.2+/-1.4)% and a longitudinal polarization fraction
(59.7+/-2.8+/-2.4)%. The measurement of a relative phase that is neither 0 nor
pi, phi_ll = 2.50+/-0.20+/-0.08 radians, favors a departure from the
factorization hypothesis. Although the decay B-->J/psi Kpi proceeds mainly via
K^*(892), there is also evidence for K^*_2(1430) and Kpi S-wave contributions.
