The magnetization configuration in two stacked micron-size ferromagnetic disks can assume different equilibrium states depending on the interfacial coupling between the disks. Here, I examine the magnetization dynamics in response to an out-of-plane field pulse for different equilibrium states. For antiferromagnetic coupling, the response spectrum generally consists of a lower-frequency part and a higher-frequency part. The former is related to the response of the core region, which has a significant in-plane response coupled to the out-of-plane one; the latter is related to spin waves generated at the edges of the disk. For a meron structure the response in the two disks to an out-of-plane pulse is also asymmetric.