Solitons are nonlinear excitations that can arise in Bose-Einstein condensates (BECs). They owe their existence to the balance between dispersion and nonlinearity. Here, we present properties and dynamics of two interacting dark-bright-dark (DBDs) as well as bright-dark-bright solitons (BDBs) of a three-component spinor F = 1 BEC in ferromagnetic, antiferromagnetic and non-spinor interacting configurations. First, we consider interaction in free space and investigate the dependence of the dynamics on the phase differences among the bright solitons, restricted to the cases ∆ϕ = {0, π}. For this purpose, static single DBD and BDB states with different phases between the components have been realized. The presence of phase-sensitive terms in the Hamiltonian sets a concrete condition, which must be fulfilled by the phases of the components in order for a static state to exist. Subsequently, the above single-soliton states are properly combined to form the initial two-DBD and two-BDB states. The different possible phase confgurations are classified based on the system's symmetries. The two-DBD system is trivially classified into two cases: bright solitons in-phase (∆ϕ = 0) or out-of-phase (∆ϕ = π). The two-BDB system is classified into three cases: in the first two, both bright-soliton pairs are in- or out-of-phase, while in the third case, one bright-soliton pair is in-phase and the other is out-of-phase. It has been found that, for both DBD and BDB systems, the in-phase and outof-phase cases exhibit similar dynamics. More specifically, in the in-phase case a repulsive effective interaction between the two solitons occurs, while in the out-of-phase case it is attractive for large distances and turns repulsive at short distances. In the third case, the dynamics are characterized by the competition between repulsion and attraction, and the presence of a breathing mode related to the violation of the aforementioned phase condition. Finally, we investigate the static properties of an in-phase pair of BDBs in the presence of a harmonic trapping potential, while varying the trap frequency and the strength of the quadratic Zeeman term.