We investigate yttrium iron garnet (YIG)/cobalt (Co) heterostructures using broadband ferromagnetic resonance (FMR). We observe an efficient excitation of perpendicular standing spin waves (PSSWs) in the YIG layer when the resonance frequencies of the YIG PSSWs and the Co FMR line coincide. Avoided crossings of YIG PSSWs and the Co FMR line are found and modeled using mutual spin pumping and exchange torques. The excitation of PSSWs is suppressed by a thin aluminum oxide interlayer but persists with a copper interlayer, in agreement with the proposed model.