In this work, we study alternating mixed-spin (s,S) Heisenberg ladders in the magnetic field h using density matrix renormalization group and linear spin-wave calculations. The h versus interchain coupling J_⊥ phase diagram for the (1/2,1) case is investigated in detail. { In particular, we demonstrate the compatibility between the critical line estimates and magnetic ordering by analyzing chains with variable values of J_⊥ and of h along the chain, J_⊥ and h scans, and considering the usual case of chains with uniform couplings}. The magnetization plateau at 1/3 of saturation magnetization, 1/3 - plateau, is observed for J_⊥>0 and in a limited range for J_⊥<0. The critical Kosterlitz-Thouless transition point, where the 1/3 - plateau closes, is identified through a finite-size analysis of the transverse spin correlation functions.