Antiferromagnetically coupled ferromagnetic thin films have recently attracted significant attention in magnonics because of the possibility to tune the spin-wave dispersion by altering the interlayer exchange coupling. To implement such coupled films in magnonic devices, a detailed understanding of the precessional dynamics of magnetization in such systems is required. Here, we present a systematic characterization of the precessional dynamics for systems with the layer magnetization going from nearly antiparallel to parallel alignment in a magnetic field. Experimentally, we have measured the ultrafast-laser-induced magnetization precession in samples with different interlayer exchange coupling strengths using the time-resolved magneto-optical Kerr effect. In our measurements, in addition to the acoustic and optical modes, an extra mode is observed that is due to the laser-induced decoupling of the two ferromagnetic layers. The observed precessional dynamics is in good agreement with our theoretical model based on the Landau-Lifshitz-Gilbert equation, and can be separated into three different field regions determined by the relationship between the Zeeman energy and the energy associated with the interlayer exchange coupling. This systematic paper, which gives a detailed description of how the interlayer exchange coupling and Zeeman energy influence the precessional dynamics, provides an important guide to implement antiferromagnetically coupled films in functional magnonic devices.