In a patrilocal residence, who leaves the household so that the married couple lives with or near the husband's parents?

Household, house, dwelling, hearth, residence.

if me and my husband both have a residence and we are married can we both file head of household?

No. Only one HOH filing status to a home or residence.

Yes, "household" is a compound word. It is made up of the words "house" and "hold" joined together to form a single word that refers to the people living together in a single residence.