IMO if its not your immediate family and you both are sick, please skip the funeral. Just send a card to the family and explain that you were too sick to be there. If you sent flowers, then that's all you need to do.
If you want, you could bring over a dish later for them for supper when you are feeling better and express your prayers/concerns, etc.
I would agree - skip the funeral and pay your respects when you are well enough to do so. I'm sure that if you send your condolences and an explanation no-one will think badly of you at all. I think the family would rather be well for the funeral than catch whatever bug you guys have got!
My thoughts and prayers are with you and the family right now - please get well soon!