Counterfactual learning for dealing with missing-not-at-random data (MNAR) is an intriguing topic in the recommendation literature since MNAR data are ubiquitous in modern recommender systems. Missing-at-random (MAR) data, namely randomized controlled trials (RCTs), are usually required by most previous counterfactual learning methods for debiasing learning. However, the execution of RCTs is extraordinarily expensive in practice. To circumvent the use of RCTs, we build an information-theoretic counterfactual variational information bottleneck (CVIB), as an alternative for debiasing learning without RCTs. By separating the task-aware mutual information term in the original information bottleneck Lagrangian into factual and counterfactual parts, we derive a contrastive information loss and an additional output confidence penalty, which facilitates balanced learning between the factual and counterfactual domains. Empirical evaluation on real-world datasets shows that our CVIB significantly enhances both shallow and deep models, which sheds light on counterfactual learning in recommendation that goes beyond RCTs.