This paper presents a statistical theory for the initial onset of multipactor breakdown in coaxial transmission lines, taking both the nonuniform electric field and random electron emission velocity into account. A general numerical method is first developed to construct the joint probability density function based on the approximate equation of the electron trajectory. The nonstationary dynamics of the multipactor process on both surfaces of coaxial lines are modelled based on the probability of various impacts and their corresponding secondary emission. The resonant assumption of the classical theory on the independent double-sided and single-sided impacts is replaced by the consideration of their interaction. As a result, the time evolutions of the electron population for exponential growth and absorption on both inner and outer conductor, in response to the applied voltage above and below the multipactor breakdown level, are obtained to investigate the exact mechanism of multipactor discharge in coaxial lines. Furthermore, the multipactor threshold predictions of the presented model are compared with experimental results using measured secondary emission yield of the tested samples which shows reasonable agreement. Finally, the detailed impact scenario reveals that single-surface multipactor is more likely to occur with a higher outer to inner conductor radius ratio.