I know what you mean. Is FH willing to ask if they will help out. I don't think they need to call your parents, but they perhaps could offere to the two of you to help out with something. Do they have the finances to be able to offer monetary help?
My FH is paying for most of the wedding and travel for us. I am paying for what I can, but he makes 3x more than I do.
However, he thinks MY parents should pay for our AHR. I expected he and I to pay for everything (although "he and I" really ends up being more him).
My Mom and Dad paid for my dress and most of the OOT bag stuff.
Other than that, both sets of parents are paying their own way for travel, but not anything else.