This study deals with a reconstruction-type superresolution problem and the accompanying image registration problem simultaneously. We propose a Bayesian approach in which the prior is modeled as a compound Gaussian Markov random field (MRF) and marginalization is performed over unknown variables to avoid overfitting. Our algorithm not only avoids overfitting, but also preserves discontinuity in the estimated image, unlike existing single-layer Gaussian MRF models for Bayesian superresolution. Maximum-marginal-likelihood estimation of the registration parameters is carried out using a variational EM algorithm where hidden variables are marginalized out, and the posterior distribution is variationally approximated by a factorized trial distribution. High-resolution image estimates are obtained through the process of posterior computation in the EM algorithm. Experiments show that our Bayesian approach with the two-layer compound model exhibits better performance both in quantitative measures and visual quality than the single-layer model.