Conversational Information Access systems have experienced widespread diffusion thanks to the natural and effortless interactions they enable with the user. In particular, they represent an effective interaction interface for conversational search (CS) and conversational recommendation (CR) scenarios. Despite their commonalities, CR and CS systems are often devised, developed, and evaluated as isolated components. Integrating these two elements would allow for handling complex information access scenarios, such as exploring unfamiliar recommended product aspects, enabling richer dialogues, and improving user satisfaction. As of today, the scarce availability of integrated datasets - focused exclusively on either of the tasks - limits the possibilities for evaluating by-design integrated CS and CR systems. To address this gap, we propose CoSRec, the first dataset for joint Conversational Search and Recommendation (CSR) evaluation. The CoSRec test set includes 20 high-quality conversations, with human-made annotations for the quality of conversations, and manually crafted relevance judgments for products and documents. Additionally, we provide supplementary training data comprising partially annotated dialogues and raw conversations to support diverse learning paradigms. CoSRec is the first resource to model CR and CS tasks in a unified framework, enabling the training and evaluation of systems that must shift between answering queries and making suggestions dynamically.