We use time-resolved magneto-optic Kerr effect and ultrathin Co/Pt transducer films to perform thermal-transport experiments with higher sensitivity and greater time resolution than typically available in studies of interfacial thermal transport by time-domain thermoreflectance. We measure the interface conductance between Pt and amorphous SiO2 using Pt/Co/Pt ferromagnetic transducer films with thicknesses between 4.2 and 8.2 nm and find an average value of GPt≈0.3GWm-2K-1. This result demonstrates that interfaces between metals and amorphous dielectrics can have a conductance corresponding to Kapitza lengths of the order of 4 nm, and are thus of relevance when engineering nanoscale devices. For thin SiO2 layers, our method also provides sensitivity to the interface conductance between SiO2 and Si and we find GSi=0.6GWm-2K-1 as the lower limit.