We present the MSP-IMPROV corpus, a multimodal emotional database, where the goal is to have control over lexical content and emotion while also promoting naturalness in the recordings. Studies on emotion perception often require stimuli with fixed lexical content, but that convey different emotions. These stimuli can also serve as an instrument to understand how emotion modulates speech at the phoneme level, in a manner that controls for coarticulation. Such audiovisual data are not easily available from natural recordings. A common solution is to record actors reading sentences that portray different emotions, which may not produce natural behaviors. We propose an alternative approach in which we define hypothetical scenarios for each sentence that are carefully designed to elicit a particular emotion. Two actors improvise these emotion-specific situations, leading them to utter contextualized, non-read renditions of sentences that have fixed lexical content and convey different emotions. We describe the context in which this corpus was recorded, the key features of the corpus, the areas in which this corpus can be useful, and the emotional content of the recordings. The paper also provides the performance for speech and facial emotion classifiers. The analysis brings novel classification evaluations where we study the performance in terms of inter-evaluator agreement and naturalness perception, leveraging the large size of the audiovisual database.