We report the spin structure of an exchange-biased ferromagnetic oxide heterostructure, La(0.67)Sr(0.33)MnO(3)/SrRuO(3), through magnetization and polarized neutron reflectometry measurements. We reveal that the magnetization reversal process of the La(0.67)Sr(0.33)MnO(3) biased layer critically depends on the frozen-in spin structure of the SrRuO(3) biasing layer during the cooling process. Furthermore, we observe unexpected double-shifted hysteresis loops of the biased layer that originates from the formation of lateral 180° magnetic domains within the biasing layer, a new mechanism not found in conventional exchange-bias systems.