This note introduces and describes the relationship between Italian families and social and health services throughout the territory, within the present social and demographic situation, with particular attention given to the difficulties families encounter when trying to access these services. The family is not only the means by which the needs of an individual are taken to the system of services but also the place where individual well-being originates, is protected and promoted. The path is determined by the culture of the family which still characterises family reality in our country, but often this is not enough for the efficiency of the services to perform as expected and desired by the population. In this work an evaluation of family discomfort is proposed, expressed by the degree of accessibility to services, by means of an indicator based on the fuzzy set theory. It is applied separately to Italy and in Triveneto, to certain family typologies, and to some important social and health services of general utility.