Companion animals (pets), especially cats and dogs, have featured regularly in the media and public discourse during the global COVID-19 pandemic, including increased demand for pet adoption and more time spent with existing pets. This qualitative study aimed to describe the experiences of Australian parents with a child under 18 years and a cat or dog. Within a broader survey, parents were asked open-ended questions about the benefits and challenges for their family of living with a cat or dog during COVID-19, and where relevant, about reasons for adopting a new pet. Data were collected between July and October 2020, during Australia’s ‘second wave’ of COVID-19, when some Australians were subject to strict physical distancing or ‘stay at home’ orders. A total of 611 parents provided at least one free-text response. Inductive template analysis was conducted on all responses; 33 unique codes were identified and mapped onto a biopsychosocial model under three themes: (i) “Trying to Stay Healthy and Well” (biological), (ii) “Comfort, Coping and Worries” (psychological), and “Spending More Time Together” (social). Findings highlight the therapeutic role of pets for families during times of change and uncertainty, as well as the significant social impact of pandemic-related restrictions on family units. Benefits included support for the family’s physical and mental health, maintenance of family routines, distraction, comfort, and pets as an opportunity to connect with others. Challenges were numerous and diverse, such as cost and access to pet care, behavioural concerns, worries about pet and child wellbeing, and reflections about the pet’s mortality. These findings demonstrate the complex and varied impacts of the pandemic on families with children and pets; some families are likely to require ongoing psychological, financial, and veterinary supports.