Off-policy evaluation (OPE) is critical for applying contextual bandit algorithms to high-stakes decision-making settings such as healthcare, where new treatment policies must be evaluated prior to deployment. Unfortunately, OPE techniques are inherently limited by the breadth of the available data, which may not be sufficient to evaluate the performance of a new policy. Recent work attempts to improve dataset coverage by adding expert-annotated counterfactual samples. However, such annotations are often imperfect and can lead to worse estimator performance than using no annotations at all. To better leverage imperfect annotations, we propose a family of OPE estimators grounded in the doubly robust (DR) framework, which combines importance sampling (IS) with a reward model (direct method, DM) for better statistical guarantees. We study three ways of incorporating counterfactual annotations. Under mild assumptions, we prove that using annotations within just the DM component yields the most desirable theoretical results. Experiments on multiple healthcare tasks, including real-world electronic health records (EHR) data, show that this strategy is most robust under misspecified reward models and inaccurate annotations. By addressing the challenges posed by imperfect annotations, this work broadens the applicability of OPE methods and facilitates safer deployment of decision-making policies in healthcare.