Sample entropy, a complexity measure that quantifies the new pattern generation rate of time series, has been widely applied to physiological signal analysis. It can effectively reflect the pattern complexity of one-dimensional sequences, such as the information contained in amplitude or period features. However, the traditional method usually ignores the interaction between amplitude and period in time series, such as electroencephalogram (EEG) signals. To address this issue, in this study, we propose a new method to describe the pattern complexity of waveform in a two-dimensional space. In this method, the local peaks of the signals are first extracted, and the variation range and the duration time between the adjacent peaks are calculated as the instantaneous amplitude and period. Then the amplitude and period sequences are combined into a two-dimensional sequence to calculate the sample entropy based on the amplitude and period information. In addition, in order to avoid the influence of the different units in the two dimensions, we use the Jaccard distance to measure the similarity of the amplitude-period bi-vectors in the waveforms, which is different from the one-dimensional method. The Jaccard distance is defined as the ratio of the different area to the combined area of two rectangles containing the amplitude-period bi-vectors in the Cartesian coordinate system. To verify the effectiveness of the method, we construct five sets of simulative waveforms in which the numbers of patterns are completely equal in one-dimensional space of amplitude or period but the numbers in two-dimensional space are significantly different (P0.00001). Simulation results show that the two-dimensional sample entropy could effectively reflect the different complexities of the five signals (P0.00001), while the sample entropy in one-dimensional space of amplitude or period cannot do. The results indicate that compared with the one-dimensional sample entropy, the two-dimensional sample entropy is very effective to describe and distinguish the complexity of interactive patterns based on amplitude and period features in waveforms. The entropy is also used to analyze the resting state EEG signals between well-matched depression patient and healthy control groups. Signals in three separated frequency bands (Theta, Alpha, Beta) and ten brain regions (bilateral: frontal, central, parietal, temporal, occipital) are analyzed. Experimental results show that in the Alpha band and in the left parietal and occipital regions, the two-dimensional sample entropy in depression is significantly lower than that in the healthy group (P0.01), indicating the disability of depression patients in generation of various EEG patterns. These features might become potential biomarkers of depressions.