During the COVID-19 pandemic, the online delivery model became the primary mode of education. With multiple pressures on society and families, mental health issues for parents have become particularly pronounced. Most of the current research has focused on the psychological state of education practitioners and children, with little attention to parents’ mental health issues. Therefore, this study explored the attitudes and coping styles of parents who experienced the process of their children being taught online over a long period and the factors influencing their mental health. This cross-sectional study was conducted between November 2021 and January 2022, using an anonymous online questionnaire to survey 1500 parents with children aged 6–13 years. The Chinese versions of the Patient Health Questionnaire Depression Scale (PHQ-9), the Parenting Stress Scale (PSS), the General Mental Health Questionnaire (GHQ-12), and the Brief Coping Style Scale (SCSQ), and a related factors questionnaire were used to survey the subjects. The normal distribution of the data was examined using the Shapiro–Wilk method. A multivariate regression analysis was conducted to identify factors significantly associated with parental mental health during the COVID-19 pandemic. Only 30.24% of parents agreed with online classes during the pandemic, and 52.28% used positive coping methods during stressful situations. Multivariate regression models identified significant factors associated with parental mental health: parent’s gender, child’s grade level, perceived stress about online classes, whether the child has ADHD, positive or negative coping styles, and subjective attitudes of support for online classes or not. The results of the study suggest that as online classes become more socially acceptable, it is necessary to be concerned about the risk of mental illness for parents and develop policies and interventions, especially for parents who adopt negative coping styles and endorse online classes. The focus should be on the stress of online classes on parents, improving the acceptance of online classes and psychological well-being, regulating the way parents deal with their children, and targeting subgroups of children with ADHD symptoms during the COVID-19 pandemic.