We present a systematic experimental and theoretical investigation of the magnonic band structure in dense arrays of both asymmetric and symmetric cross-section trilayered Fe(10 nm)/Cu(t)/Py(10 nm) nanowires (NWs). The Cu spacer thickness (t) is varied in the range between 0 and 10 nm. The frequency dispersion of collective spin-wave excitations in the above trilayered NW arrays has been studied by the Brillouin light-scattering technique while sweeping the wave vector perpendicularly to the nanowire length over four Brillouin zones of the reciprocal space. The experimental results have been quantitatively reproduced by an original numerical model that includes a two-dimensional Green's function description of the dipole field of the dynamic magnetization and exchange coupling between the layers. We found that, depending on t, the Py and Fe magnetic layers within the same nanowire are coupled by either the interlayer exchange or dipolar interactions. This has an impact on both the magnetization reversal and the collective dynamical properties of the artificial crystal. In particular, it is possible to stabilize a magnetization configuration where the layer magnetization vectors point in the same or in the opposite direction over a field range that varies with the Cu thickness. In addition, several modes are detected whose propagation properties (i.e., stationary or dispersive) through the array depend on static magnetization configuration as well as on the relative phase (in-phase or out-of-phase) of dynamic magnetizations between the two layers within the same nanowire.