Signing up household type memberships
One approach would be to extend to code which makes the 'on behalf of Organisation' approach work for Households as well. 

The membership type would be set up so that an individual 'inherits' the membership based on a specified relationship.

When an Individual signs up they either be given the option of selecting 'on behalf of', or the 'household' membership page would be set up to require it.

The outcome of a new membership would be that the individual is created, a household is created, the membership 'belongs' to the household, a permissioned* relationship would be created between the individual and the household, and due to that relationship the individual would 'inherit' the membership provided in the settings of the Membership Type.


my understanding of the 'on behalf of Organisation' code is that for the individual to be able to renew on behalf of the organisation (ie for their Organisation to prefill on the form if the user is logged in or using a checksum link) the individual is set up with the 'employee of' Relationship, they are also set as 'current employee' and the relationship is set so the individual is 'permissioned over the organisation'.


For a household equivalent, there is no equivalent for 'current employee' so the solution would need to step around that but that sounds fairly trivial.