The Grossman model has been extended recently in order to take account of the fact that most people lead their lives in a family--using frameworks in which family members, respectively, (a) have common preferences and (b) are Nash-bargainers. These models, however, do not consider individual incentives for behaving strategically. In the model presented in this paper, spouses interact strategically both in the production of own health and in the production of health of other family members. We analyse, inter alia, the impact on the distribution of health of changes in family policies, such as child allowance and custody rules.