We report on the interfacial magnetic coupling in manganite bilayers of collinear ferromagnetic La0.7Sr0.3MnO3 and noncollinear multiferroic TbMnO3. Exchange bias is observed at the Néel temperature of TbMnO3 (,41 K) due to the onset of long-range antiferromagnetic ordering in the Mn spin sublattice. Interestingly, an anomalous plateau of exchange bias emerges at the ordering temperature of Tb spins (,10 K), and we ascribe this unique feature to the strong coupling between Tb and Mn spin sublattices in TbMnO3, which in turn influences the magnetic coupling across the interface. On the other hand, the enhancement of coercivity in La0.7Sr0.3MnO3/TbMnO3 shows monotonous temperature dependence. Our results illustrate a strong interfacial magnetic interaction at the La0.7Sr0.3MnO3/TbMnO3 interface, highlighting the roles of competing spin orders, magnetic frustration, and coupling between multiple spin sublattices in artificial collinear/noncollinear spin heterostructures.