We present a detailed investigation of the electronic phase diagram of effectively charge compensated Ba_1-xK_x(Fe_1-yCo_y)₂As₂ with x/2 ≈ y. Our experimental study by means of x-ray diffraction, Mössbauer spectroscopy, muon spin relaxation and ac-susceptibility measurements on polycrystalline samples is complemented by density functional electronic structure calculations. For low substitution levels of x/2 ≈ y ≤ 0.13, the system displays an orthorhombically distorted and antiferromagnetically ordered ground state. The low-temperature structural and magnetic order parameters are successively reduced with increasing substitution level. We observe a linear relationship between the structural and the magnetic order parameter as a function of temperature and substitution level for x/2 ≈ y ≤ 0.13. At intermediate substitution levels in the range between 0.13 and 0.19, we find superconductivity with a maximum T_c of 15 K coexisting with static magnetic order on a microscopic length scale. For higher substitution levels x/2 ≈ y ≥ 0.25, a tetragonal nonmagnetic ground state is observed. Our DFT calculations yield a significant reduction of the Fe 3d density of states at the Fermi energy and a strong suppression of the ordered magnetic moment in excellent agreement with experimental results. The appearance of superconductivity within the antiferromagnetic state can by explained by the introduction of disorder due to nonmagnetic impurities to a system with a constant charge carrier density.