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Mixed-valent Ba₂Mn²⁺Mn₂³⁺(SeO₃)₆ crystallizes in a monoclinic <i>P2</i>₁<i>/c</i> structure and has honeycomb layers of Mn³⁺ ions alternating with triangular layers of Mn²⁺ ions. We established the key parameters governing its magnetic structure by magnetization <i>M</i> and specific heat <i>C</i>_p measurements. The title compound exhibits a close succession of a short-range correlation order at <i>T_corr</i> = 10.1 ± 0.1 K and a long-range Néel order at <i>T_N</i> = 5.7 ± 0.1 K, and exhibits a metamagnetic phase transition at <i>T < T_N</i> with hysteresis most pronounced at low temperatures. The causes for these observations were found using the spin exchange parameters evaluated by density functional theory calculations. The title compound represents a unique case in which uniform chains of integer spin Mn³⁺ (<i>S</i> = 2) ions interact with those of half-integer spin Mn²⁺ (<i>S</i> = 5/2) ions.