We propose a generalized Floquet Hamiltonian method that is applicable to laser-induced molecular dynamics including nonperiodicity arising from time dependence of laser parameters and nuclear kinematic effects. Effects from these two types of nonperiodicity are formulated as generalized nonadiabatic transitions and treated in a unified manner. In this unified treatment, the field-induced dynamics of a molecule is mapped onto an effective nonadiabatic dynamics. An analog of the gradient approximation to the field-free nonadiabatic dynamics thus naturally follows and the relevant validity conditions are also formulated. Full-quantum-type numerical implementation of this method is applied first to the field-induced dynamics of H 2 + /D 2 + within a two-state model and second to that of LiF based on the ab initio potential-energy surfaces. With the H 2 + /D 2 + calculations, we confirm the validity of our formalism by reproducing the previously reported dissociation probabilities, which represent the phenomena of bond softening and bond hardening, including the "inverse bond-hardening effect" that has been identified in the present study. In the calculations of LiF, we realize full generalized ab initio Floquet analysis including the intrinsic nuclear derivative coupling. The effects of nuclear derivative couplings are assessed by directly comparing the calculations with and without the couplings. The present method, giving a simple and clear view of field-induced and kinematically induced nonadiabatic transitions, appears to be promising for the study of ab initio laser-induced dynamics of a system with nuclear derivative couplings.