Evidence from past economic crises indicates that recessions often affect men's and women's employment differently, with a greater impact on male-dominated sectors. The current COVID-19 crisis presents novel characteristics that have affected economic, health and social phenomena over wide swaths of the economy. Social distancing measures to combat the spread of the virus, such as working from home and school closures, have placed an additional tremendous burden on families. Using new survey data collected in April 2020 from a representative sample of Italian women, we analyse jointly the effect of COVID-19 on the working arrangements, housework and childcare of couples where both partners work. Our results show that most of the additional workload associated to COVID-19 falls on women while childcare activities are more equally shared within the couple than housework activities. According to our empirical estimates, changes to the amount of housework done by women during the emergency do not seem to depend on their partners' working arrangements. With the exception of those continuing to work at their usual place of work, all of the women surveyed spend more time on housework than before. In contrast, the amount of time men devote to housework does depend on their partners' working arrangements: men whose partners continue to work at their usual workplace spend more time on housework than before. The link between time devoted to childcare and working arrangements is more symmetric, with both women and men spending less time with their children if they continue to work away from home. For home schooling, too, parents who continue to go to their usual workplace after the lockdown are less likely to spend greater amounts of time with their children than before. Similar results emerge for our sample of women not working before the emergency. Finally, analysis of work-life balance satisfaction shows that working women with children aged 0-5 are those who say they find balancing work and family more difficult during COVID-19. The work-life balance is especially difficult to achieve for those with partners who continue to work outside the home during the emergency.