This paper examines whether a tax on unhealthy food and a nudge are suitable to promote families healthy eating. We consider, in a theoretical model, an economy composed of two types of family that differ in their income and their nutritional knowledge, which reflects their degree of misperception of the future health effects of diet, and choose their consumption according to their perceived utility. We find that the decentralized solution of taxation on unhealthy good achieves the first-best optimum if and only if it is possible for the central planner to implement a targeted tax policy. Investigating the case of a mixed policy, we find that taxation of unhealthy food and nudge are probably complementary public policy instruments to promote family healthy eating. The mixed policy reduces both the perception and income gaps between the two family types.