The number of older adults who are homebound with depressive symptoms is increasing. Due to their homebound status, they have limited access to trained mental healthcare support, which leaves this support often to untrained family caregivers. To increase access, a growing interest is placed on using technology-mediated solutions, such as voice-assisted intelligent personal assistants (VIPAs), to deliver mental health services to older adults. To better understand how older adults and family caregivers intend to interact with a VIPA for mental health interventions, we conducted a participatory design study during which 6 older adults and 7 caregivers designed VIPA-human dialogues for various scenarios. Using conversation style preferences as a starting point, we present aspects of human-likeness older adults and family caregivers perceived as helpful or uncanny, specifically in the context of the delivery of mental health interventions, which helps inform potential roles VIPAs can play in mental healthcare for older adults.