The lateral distributions of depth-averaged velocity in open compound channels with emerged and submerged vegetated floodplains were analyzed based on the analytical solution of the depth-integrated Reynolds-Averaged Navier-Stokes equation with a term to account for the effects of vegetation. The three cases considered for open channels were two-stage rectangular channel with emerged vegetated floodplain, rectangular channel with submerged vegetated corner, and two-stage rectangular channel with submerged vegetated floodplain, respectively. To predict the depth-averaged velocity with submerged vegetated floodplains, we proposed a new method based on a two-layer approach where flow above and through the vegetation layer was described separately. Moreover, further experiments in the two-stage rectangular channel with submerged vegetated floodplain were carried out to verify the results. The analytical solutions of the cases indicated that the corresponding analytical depth-averaged velocity distributions agree well with the simulated and experimental prediction. The analytical solutions of the cases with theoretical foundation and without programming calculation were reasonable and applicable, which were more convenient than numerical simulations. The analytical solutions provided a way for future researches to solve the problems of submerged vegetation and discontinuous phenomenon of depth-averaged velocity at the stage point for compound channels. Understanding the hydraulics of flow in compound channels with vegetated floodplains is very important for supporting the management of fluvial processes.