The lowest-order theory for the weak non-monotonic double layers (NDLs) and shock-like structures (SLSs) in multispecies plasma (including both positive and negative ions) is described and is applied to the fluid-Vlasov system that consists of two component ions and two types of electrons. The analytical results show that NDLs and SLSs exhibit opposite characteristics to the case of ordinary shock structures and solitons: they slow down as the amplitude and the scale length increase, whereas the ordinary shock structures and solitons speed up. The relation between the propagation velocities of NDLs and the masses of multiple ion species suggest that the lowest propagation velocity of NDLs may be directly related to the mass of the negative ions.