Infant language learning depends on the distribution of co-occurrences "within" language--between words and other words--and "between" language content and events in the world. Yet infant-directed speech is not limited to words that refer to perceivable objects and actions. Rather, caregivers' utterances contain a range of syntactic forms and expressions with diverse attentional, regulatory, social, and referential functions. We conducted a distributional analysis of linguistic content types at the utterance level, and demonstrated that a wide range of content types in maternal speech can be distinguished by their distribution in sequences of utterances and by their patterns of co-occurrence with infants' actions. We observed free-play sessions of 38 12-month-old infants and their mothers, annotated maternal utterances for 10 content types, and coded infants' gaze target and object handling. Results show that all content types tended to repeat in consecutive utterances, whereas preferred transitions between different content types reflected sequences from attention-capturing to directing and then descriptive utterances. Specific content types were associated with infants' engagement with objects (declaratives, descriptions, object names), with disengagement from objects (talk about attention, infant's name), and with infants' gaze at the mother (affirmations). We discuss how structured discourse might facilitate language acquisition by making speech input more predictable and/or by providing clues about high-level form-function mappings.