Structural health monitoring (SHM) is crucial in the early stage of damage formation for the life-cycle service of offshore structures. The influence of soils on vibration-based damage detection systems in offshore structures is a critical issue but has received less attention in previous literature. Due to the complexity of offshore structures and their exposure to diverse loads, simultaneous compound damages across different components can occur, posing a significant challenge for damage detection. Existing methods often treat compound damage as a distinct type of damage, independent of corresponding single damages. Nonetheless, in cases where damages arise concurrently, the distinct characteristics of each individual damage are evident independently within the vibration signals. This study presents a new approach for detecting both single and compound damage in offshore structures considering soil interaction using vibration data. The approach combines Wavelet Transform (WT) with a Multiple Interference Deep Convolutional Neural Network (MIDCNN) to effectively learn desired features and detect damage in these structures. The MIDCNN model is trained on time-frequency data from healthy and single damage states, without incorporating time-frequency data from compound damage during training. In the testing phase, the MIDCNN model intelligently alarms healthy, single damage states, and an untrained compound damage state based on predefined probabilistic conditions derived from the MIDCNN output probabilities. The time-frequency data are generated using the WT method, which is adept at capturing the natural characteristics of the structure while minimizing the influence of noise or irrelevant components. The proposed approach is validated using measured data from a laboratory-scale offshore monopile model with soil interaction. The findings demonstrate that the proposed method is more robust than other methods in extracting features and classifying various states, including healthy, single and compound damages.