Students who take lab courses engage in active, collaborative learning that has the potential to teach scientific thinking skills while also stimulating students' interest in science and developing their self-efficacy. We describe different types of collaboration in terms of the mutuality of engagement they represent, and investigate how these different types of collaboration impacted student interest and self-efficacy in introductory physics labs. We surveyed college physics students about their beliefs and experiences regarding working with a lab partner. We find that when asked explicitly about what they valued in a lab partner, a majority of students noted that they wanted a "fair split" of the work. However, we find that students experienced improved physics interest and self-efficacy when they participated equally in all aspects of the lab, such as operating the apparatus and recording the data, which is a different form of mutuality of engagement. This form of participation disproportionately benefited women, a traditionally disadvantaged group in physics labs. Our findings suggest that students' physics interest and self-efficacy might be positively impacted in lab courses that are designed to ensure that students participate equally in all aspects of the lab work, as opposed to lab courses in which students split up their work inequitably, as they might prefer to do.