I am part of a family plan for which someone else is the organizer. However I would like to be able to make separate purchases with my own credit card independently from the family plan. How can I set this up?

It's working as designed, the family organiser takes responsibility for the family's purchases !! If you want to leave feedback to Apple about it use the feedback pages : http://www.apple.com/feedback/

I don't see that as a problem. With my family. It is my father and me that are linked. I am 38. I should be able to use my own credit card rather than having to go buy a special iTunes card just to carry a balance.

Try thinking it through systematically. Think about Apple. Think about the media companies who get to tell Apple if they may sell their recordings. Think about how media sales would be affected if any loose association of 6 people could become a family.

Actually, you're asking a lot. Only a few years ago there was no sharing at all in any form. Right now we're probably back status quo to where things were before digital media when you had families with record collections. If Susan took the only copy of the BeeGees with her to college then the rest of the family couldn't listen to it without buying their own copy. If you took the family's only copy of AC/DC into your room nobody else could play it a the same time unless you blasted out the volume. I know when I left home I bought at least 20 albums we had at home so I could have a copy.

That is messed up. Two adults in a family sharing plan should be able to use their own cards!!! Apple needs to change this!!!

Yes, they will still get the emailed receipt : Family purchases and payments - Apple Support

You will have to leave the family share if you want to use your own credit card - in family share members (but not the organiser) can use a balance on their account, otherwise the organiser's card will be charged

Yes, if you have a balance on your account your purchases will use it - the organiser's card will only be charged if your balance doesn't cover a purchase (in which case only the extra amount be charged to their card)

Two adults in a family sharing plan should be able to use their own cards

What's then to prevent you and me from becoming a "family" so we can share each other's purchases?

Will the Family organizer be able to see my purchase if I use a gift card? Are they alerted in any way if I cover the total amount of the purchase? Thanks