  We study the magnetic phase diagram of two coupled mixed-spin $(1,{1/2})$
Heisenberg chains as a function of the frustration parameter related to
diagonal exchange couplings. The analysis is performed by using spin-wave
series and exact numerical diagonalization techniques. The obtained phase
diagram--containing the Luttinger liquid phase, the plateau phase with a
magnetization per rung $M=1/2$, and the fully polarized phase--is closely
related to the generic $(J/U,\mu/U)$ phase diagram of the one-dimensional boson
Hubbard model.
