We examine the conditions of the plasma along a sample of ’ classical ’ Herbig-Haro ( HH ) jets located in the Orion and Vela star forming regions , through combined optical-infrared spectral diagnostics . Our sample includes HH 111 , HH 34 , HH 83 , HH 73 , HH 24 C/E , HH 24 J , observed quasi-simultaneously and in the same manner at moderate spatial/spectral resolution . Once inter-calibrated , the obtained spectra cover a wide wavelength range from 0.6 - 2.5 \mu m , including many transitions from regions of different excitation conditions . This allows us to probe the density and temperature stratification which characterises the cooling zones behind the shock fronts along the jet . From the line ratios we derive the variation of the visual extinction along the flow , the electron density and temperature ( n _ { e } and T _ { e } ) , the hydrogen ionisation fraction x _ { e } , and the total density n _ { H } in the emission region of different lines . The knowledge of such parameters is essential for testing existing jet models and for planning follow-up high-angular resolution observations . From the diagnostics of optical forbidden lines we find , on average , that in the examined jets , in the region of optical emission , n _ { e } varies between 50 cm ^ { -3 } and 3 10 ^ { 3 } cm ^ { -3 } , x _ { e } ranges between 0.03 and 0.6 , and the electron temperature T _ { e } is \sim 1.3 10 ^ { 4 } K in the HH 111 and HH 34 jets , while it appears to be higher ( 1.8 10 ^ { 4 } K on average ) in the other examined jets . The electron density and temperature derived from [ Fe ii ] lines , turn out to be , respectively , higher and lower in comparison to those determined from optical lines , in agreement with the fact that the [ Fe ii ] lines arise in the more compressed gas located further from the shock front . An even denser component in the jets , with values of n _ { e } up to 10 ^ { 6 } cm ^ { -3 } is detected using the ratio of Calcium lines . The derived physical parameters are used to estimate the depletion onto dust grains of Calcium and Iron with respect to solar abundances . This turns out to be quite substantial , being between 70 % and 0 % for Ca and \sim 90 % for Fe . This leads us to suggest that the weak shocks present in the beams are not capable of completely destroying the ambient dust grains , confirming previous theoretical studies . We then derive the mass flux rates , \dot { M } _ { jet } , in the flows using two independent methods . Taking into account the filling factor of the emitting gas , \dot { M } _ { jet } is on average 5 10 ^ { -8 } M _ { \odot } yr ^ { -1 } . The associated linear momentum fluxes ( \dot { P } _ { jet } = v _ { jet } \dot { M } _ { jet } ) are higher than , or of the same order as , those measured in the coaxial molecular flows , where present , suggesting that the flows are jet driven . Finally , we discuss differences between jets in our sample . In general , we find that higher ionisation and electron temperatures are associated with less dense jets . The comparison suggests that the shock mechanism exciting the knots along the flows has the same efficiency in all the examined objects , and the observed differences are consistent with the different densities , and hence cooling rates , found in the various flows .