In recommender systems, usually the ratings of a user to most items are missing and a critical problem is that the missing ratings are often missing not at random (MNAR) in reality. It is widely acknowledged that MNAR ratings make it difficult to accurately predict the ratings and unbiasedly estimate the performance of rating prediction. Recent approaches use imputed errors to recover the prediction errors for missing ratings, or weight observed ratings with the propensities of being observed. These approaches can still be severely biased in performance estimation or suffer from the variance of the propensities. To overcome these limitations, we first propose an estimator that integrates the imputed errors and propensities in a doubly robust way to obtain unbiased performance estimation and alleviate the effect of the propensity variance. To achieve good performance guarantees, based on this estimator, we propose joint learning of rating prediction and error imputation, which outperforms the state-of-the-art approaches on four real-world datasets.