There are a couple of ways you could approach it:
1) You could store the Family itself as the contact with the membership, and also create contact records for each of the other individual family members, then use relationships to link the individuals to the Family contact to indicate that they might be using the Family Membership (this is how most clients handle Family Memberships in Sumac).
2) You could store the Family itself as the contact with the membership, or store a contact record for a primary, Head of Household contact. Then use a Notes field to indicate the individual family members who might use the Family Membership.
In either case above, the Membership itself will be linked to the contact who actually purchased the Family Membership (i.e. either the Family contact, or the Head of Household contact).
3) You can activate up to four (4) additional Contact fields in Membership records. This allows you to add even more contacts to a Membership record, which is ideal for Family Memberships where perhaps three or four family members are using the same Membership. If you wish to activate these fields, log into Sumac as an Administrator. Click Utilities > Customize Database > Field Preferences. Under Specialized, click "Membership." Next to the "Member 1-4" fields, ensure there is no "X" in the "Hide" option for these fields. Click OK, then restart Sumac to save these changes.