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Humor is a substantial element of human social behavior, affect, and cognition. Its automatic understanding can facilitate a more naturalistic human-AI interaction. Current methods of humor detection have been exclusively based on staged data, making them inadequate for "real-world" applications. We contribute to addressing this deficiency by introducing the novel Passau-Spontaneous Football Coach Humor (Passau-SFCH) dataset, comprising about 11 hours of recordings. The Passau-SFCH dataset is annotated for the presence of humor and its dimensions (sentiment and direction) as proposed in Martin's Humor Style Questionnaire. We conduct a series of experiments employing pretrained Transformers, convolutional neural networks, and expert-designed features. The performance of each modality (text, audio, video) for spontaneous humor recognition is analyzed and their complementarity is investigated. Our findings suggest that for the automatic analysis of humor and its sentiment, facial expressions are most promising, while humor direction can be best modeled via text-based features. Further, we experiment with different multimodal approaches to humor recognition, including decision-level fusion and MulT, a multimodal Transformer approach. In this context, we propose a novel multimodal architecture that yields the best overall results. Finally, we make our code publicly available at https://www.github.com/lc0197/passau-sfch. The Passau-SFCH dataset is available upon request.