In modern complex mechanical systems, machine faults typically occur in multiple components simultaneously, and the domain of collected sensor data changes continuously due to variations in operating conditions. Deep learning-based fault diagnosis approaches have recently been enhanced to address these real-world industrial challenges. Comprehensive labeled data covering compound fault scenarios and multi-domain conditions are crucial for exploring these issues. However, existing multi-domain datasets focus on a limited range of operating conditions, such as motor rotating speeds and loads. This limits their applicability to real-world industrial scenarios. To bridge this gap, we present a novel multi-domain dataset that incorporates these basic conditions and extends to various bearing types and compound machine faults. The deep groove ball bearing, the cylindrical roller bearing, and the tapered roller bearing were utilized to provide data that reflect diverse mechanical interactions between the shaft and the bearing. Vibration data were collected using a USB digital accelerometer at two sampling rates and six rotating speeds, encompassing three single bearing faults, seven single rotating component faults, and 21 compound faults of the bearing and rotating component. Additionally, the dataset provides spectrograms of vibration data using short-time Fourier transform (STFT) for data-driven analysis with a 2-D input. This dataset encompasses more complex compound fault and domain shift problems than those presented in conventional public vibration datasets, thereby aiding researchers in studying intelligent fault diagnosis methods based on deep learning.