This paper considers the problem of detecting and tracking multiple maneuvering targets, which suffers from the intractable inference of high-dimensional latent variables that include target kinematic state, target visibility state, motion mode-model association, and data association. A unified message passing algorithm that combines belief propagation (BP) and mean-field (MF) approximation is proposed for simplifying the intractable inference. By assuming conjugate-exponential priors for target kinematic state, target visibility state, and motion mode-model association, the MF approximation decouples the joint inference of target kinematic state, target visibility state, motion mode-model association into individual low-dimensional inference, yielding simple message passing update equations. The BP is exploited to approximate the probabilities of data association events since it is compatible with hard constraints. Finally, the approximate posterior probability distributions are updated iteratively in a closed-loop manner, which is effective for dealing with the coupling issue between the estimations of target kinematic state and target visibility state and decisions on motion mode-model association and data association. The performance of the proposed algorithm is demonstrated by comparing with the well-known multiple maneuvering target tracking algorithms, including interacting multiple model joint probabilistic data association, interacting multiple model hypothesis-oriented multiple hypothesis tracker and multiple model generalized labeled multi-Bernoulli.