Although laughter has gained considerable interest from a diversity of research areas, there still is a need for laughter specific databases. We present the Multimodal Laughter during Interaction (MULAI) database to study the expressive patterns of conversational and humour related laughter. The MULAI database contains 2 hours and 14 minutes of recorded and annotated dyadic human-human interactions and includes 601 laughs, 168 speech-laughs and 538 on- or offset respirations. This database is unique in several ways; 1) it focuses on different types of social laughter including conversational- and humour related laughter, 2) it contains annotations from participants, who understand the social context, on how humourous they perceived themselves and their interlocutor during each task, and 3) it contains data rarely captured by other laughter databases including participant personality profiles and physiological responses. We use the MULAI database to explore the link between acoustic laughter properties and annotated humour ratings over two settings. The results reveal that the duration, pitch and intensity of laughs from participants do not correlate with their own perception of how humourous they are, however the acoustics of laughter do correlate with how humourous they are being perceived by their conversational partner.