as a parent, I would definitely assume we both were invited at the expense of the host/ess unless it was specified as a dropoff party.
It is no different than a party at someone's home or at chuck E cheese or whatever. If you expect the parents to pay their own way anywhere, you really need to make that clear on the invite though so they can decide if they want to attend. ofr myself, if an invite said that only one of us were "comped" for lack of a better word, and the other would not be, we simply would not attend unless it were for a good friends and I knew they had money problems or soemthing...
Sorry to sound like miss manners, but it makes me think of an acquaintance who had her daughter's party as a potluck luncheon.. we all just thought it was tacky to do that. You chose the venue, you should pay the tab, for both parents if they want to come...
just my $4.95 (inflation)