As part of the “Circuit-breaker” social distancing measure to address COVID-19, the government of Singapore closed schools and workplaces from April to May 2020. Although this helped reduce transmission rates, for working parents, this period had been a challenging experience of working from home while providing care for children full-time. Problems in the work-home interface can have a significant impact on parenting and marital harmony. We analyzed data from 201 married and employed parents in Singapore using online surveys. Latent profile analysis was used to identify profiles of parents’ work–family balance (WFB) and spousal and employer support. Linear regression was used to examine links between profiles with parenting stress and marital conflicts. Results indicated three distinct profiles of WFB and social support levels: (a) Strong (43%), (b) Moderate (38%), and (c) Poor (19%). Mothers were more likely than fathers to be in the Moderate and Poor profiles. One key finding is that profiles characterized by poorer WFB were found to be linked with higher parenting stress and increased marital conflicts. There are important variations in parents’ abilities to balance work and family and levels of social support received. Lock-downs can affect parenting and marital harmony especially for parents with poor WFB and weak social support. Any attention given to supporting working parents is vital and urgent to counter any problems in the work–family interface during a lockdown.