Is it possible to link two (or more) members in a joint/household membership and create a single label for joint/household memberships?

You can create membership type(s) with "Household Members" as the Relationship Type — see Admin CiviCRM >> CiviMember >> MembershipTypes>> Relationship Type. I don't think this quite does what you want, but you might play with that a bit and see what the search on members returns if you grant that type of membership to a Household entity.