For a nonstationary process which has a time-varying mean, a time-varying variance, or both, it can be difficult to detect incipient disturbances which may be hidden by the time-varying process variations. Besides, stationary and nonstationary characteristics may coexist in complex industrial processes which, however, have not been studied for process monitoring. In the present work, a triple subspace decomposition based dissimilarity analysis algorithm is developed to detect incipient abnormal behaviors in complex industrial processes with both stationary and nonstationary hybrid characteristics. The novelty is how to comprehensively separate the stationary and nonstationary process characteristics and describe them, respectively. First, a stationarity evaluation and separation strategy is proposed to decompose the data space into three subspaces, revealing the linear stationary process characteristics, the nonlinear stationary process characteristics, and the final nonstationary process characteristics. Then, a triple subspace distribution monitoring strategy is proposed to quantitatively evaluate the changes of linear and nonlinear stationary and nonstationary distribution structures. The paper demonstrates that the new method has better performance in detection of incipient abnormal behaviors that are responsible for distortion of the underlying covariance structure in industrial processes with both stationary and nonstationary hybrid process characteristics. Its feasibility and performance are illustrated with two case studies of real industrial processes.