The associated production of neutral Higgs bosons with the Z 0 gauge boson ( h 0 Z 0 , H 0 Z 0 ) is investigated in the context of the future linear colliders, such as the ILC and CLIC, within the general two-Higgs-doublet model (2HDM). We compute the corresponding cross section for the processes e + e − → Z 0 h 0 / Z 0 H 0 at one-loop, including the full set of corrections at O ( α 3 e w ) together with the leading O ( α 4 e w ) terms, in full consistency with the available theoretical and phenomenological constraints. We find that the wave-function corrections to the external Higgs fields are the dominant source of the quantum effects, which turn out to be large and negative (e.g., δ σ / σ ∼ − 20 % / − 60 % ) in all the √ s range, and located predominantly in the region around tan  β ∼ 1 and moderate values of the parameter λ 5 (being λ 5 < 0 ). This behavior can be ultimately traced back to the enhancement potential of the triple Higgs-boson self-couplings, a trademark feature of the 2HDM with no counterpart in the Higgs sector of the minimal supersymmetric standard model. Even under this substantial depletion of the one-loop-corrected signal (which is also highly distinctive with respect to the SM expectation for e + e − → Z 0 H ), the predicted Higgs-strahlung rates comfortably reach a few tens of femtobarn, which means barely ∼ 10 3 - 10 4 events per 500     fb − 1 of integrated luminosity. Because of their great complementarity, we argue that the combined analysis of the Higgs-strahlung events ( h 0 Z 0 , H 0 Z 0 ) and the previously computed one-loop Higgs-pair production processes ( H 0 A 0 ) could be instrumental to probe the structure of the Higgs sector at future linac facilities.