This work presents a new theory of multipactor under multicarrier signals for parallel-plate geometries, assuming a homogeneous electric field and one-dimensional electron motion. It is the generalization of the nonstationary multipactor theory for single-carrier signals [S. Anza,Phys. Plasmas 17, 062110 (2010)]. It is valid for multicarrier signals with an arbitrary number of carriers with different amplitude, arbitrary frequency, and phase conditions and for any material coating. This new theory is able to model the real dynamics of the electrons during the multipactor discharge for both single and double surface interactions. Among other parameters of the discharge, it calculates the evolution in time of the charge growth, electron absorption, and creation rates as well as the instantaneous secondary emission yield and order. An extensive set of numerical tests with particle-in-cell software has been carried out in order to validate the theory under many different conditions. This theoretical development constitutes the first multipactor theory which completely characterizes the multipactor discharge for arbitrary multicarrier signals, setting the first step for further investigations in the field.