Alleviating relative poverty is a fundamental prerequisite for achieving common prosperity. This study constructs a multidimensional relative poverty index system, incorporating factors such as mental health and environmental quality, and adopts the A-F poverty framework system. Utilizing data from the China Family Panel Studies (CFPS) and employing the neural network random weight (NNRW) method from machine learning, it precisely measures and decomposes the breadth, depth, and intensity levels of multidimensional relative poverty among urban-rural and regional residents in China. The research finds that regardless of urban-rural or regional disparities, as the dimensions of relative poverty increase, the breadth, depth, and intensity indices of multidimensional relative poverty all decrease, indicating a gradual reduction in the number of residents experiencing extreme multidimensional relative poverty. Meanwhile, residents’ multidimensional relative poverty indices exhibit a “high in the west and low in the east” trend, with the overall level of multidimensional relative poverty among residents roughly equivalent to that of the central regions. Rural residents’ multidimensional relative poverty levels are significantly higher than urban residents’, and rural residents’ multidimensional relative poverty levels are similar to those of the western regions; while urban residents’ multidimensional relative poverty levels are roughly equivalent to those of the eastern regions. Additionally, the decomposition results of the multidimensional relative poverty index show that factors such as financial products, living environment, durable goods, and per capita net income are the main reasons for relative poverty among urban-rural and regional residents, but the contribution rates of poverty determinants to the breadth, depth, and intensity differ. The research conclusions provide theoretical references and policy bases for formulating long-term mechanisms to address multidimensional relative poverty.