In this article, the adaptive online state smoothing problem is studied for a Markov jump system where the measurement noise covariance matrix (MNCM) is unknown. To address this problem, two adaptive interacting multiple model online smoothing algorithms are proposed to jointly estimate the target state and the unknown MNCM. Specifically, the article quantitatively examines the impact of noise covariance matrix mismatch on state estimation and theoretically demonstrates that the joint posterior distribution of the target state and the MNCM cannot be analytically obtained using the original variational Bayesian (VB) approach. To overcome this limitation, an approximate VB method is introduced, which utilizes the approximated state distribution obtained through the moment-matching method to update the MNCM. In addition, the convergence criterion of the proposed adaptive smoothing algorithms is designed. Finally, the estimation consistency of MNCM is analyzed. A maneuvering target tracking simulation example is presented to evaluate the effectiveness and applicability of the proposed adaptive algorithms.