A self-consistent theory involving Maxwell’s equations and a density-matrix linear-response theory is solved for an electromagnetically coupled doped graphene micro-ribbon array (GMRA) and a quantum well (QW) electron gas sitting at an interface between a half-space of air and another half-space of a doped semiconductor substrate, which supports a surface-plasmon mode in our system. The coupling between a spatially modulated total electromagnetic (EM) field and the electron dynamics in a Dirac-cone of a graphene ribbon, as well as the coupling of the far-field specular and near-field higher-order diffraction modes, are included in the derived electron optical-response function. Full analytical expressions are obtained with nonlocality for the optical-response functions of a two-dimensional electron gas and a graphene layer with an induced bandgap, and are employed in our numerical calculations beyond the long-wavelength limit (Drude model). Both the near-field transmissivity and reflectivity spectra, as well as their dependence on different configurations of our system and on the array period, ribbon width, graphene chemical potential of QW electron gas and bandgap in graphene, are studied. Moreover, the transmitted $E$-field intensity distribution is calculated to demonstrate its connection to the mixing of specular and diffraction modes of the total EM field. An externally tunable EM coupling among the surface, conventional electron-gas and massless graphene intraband plasmon excitations is discovered and explained. Furthermore, a comparison is made between the dependence of the graphene-plasmon energy on the ribbon’s width and chemical potential in this paper and the recent experimental observation given by [Nat. Nanotechnol. 6, 630 – 634 (2011)] for a GMRA in the terahertz-frequency range.