@mmorrison5 , as a general matter, "It Depends".
If the payment is for a fixed sum agreed (for the purposes of defraying the additional cost), then it is income to you and taxed as such ( "Other income" with no self-employment taxes ).
If you are in the business of hosting ( students and/or others ) then the income can be recognized on schedule-C and allowable expenses can offset the income -- self-employment taxes also apply
If payment was gift ( i.e. there was no agreement and/no requirement to pay but the guest family wanted to help), then it is NOT income and therefore not taxable, even if the family is foreign.
That is my view/opinion.
pk
pk