Do your family members not live in an EU/EEA country or Switzerland? In that case they are not entitled to a European Health Insurance Card (EHIC). To cover any medical costs incurred while you are staying in those countries, you need to take out extra insurance or travel insurance.
NB: You can obtain an EHIC yourself from your health insurer, as you have Dutch health insurance. With this EHIC you are entitled to medical care in other EU countries.