A household, as far as SNAP Benefits are concerned, can be many of types of living arrangements.
Obviously, a household can be a traditional family, with a married couple only, or a married couple with children, but other living situations also qualify as a household for SNAP eligibility as well.
A household can be a single person who lives alone, or a group of people who live in the same home, purchase their food together, and share their meals. The group of people does not need to be related in order to qualify as a household for food stamp eligibility purposes.
If you live in a situation where you buy your own food for yourself and/or your children, but you live with other people who buy their food separately from you, you should be able to apply for food stamps as a completely separate household.
If you apply as a separate household, you may be able to get more food stamp benefits because the income of the other members of the household will not be calculated.
As far as SNAP eligibility goes, the less income you have, the more food stamps you will be eligible for in each monthly allotment.