I have not used CHFA. My daughter used it, and yes, it comes with a higher % interest. Each different program comes with a variety of conditionals.
"Would a FHA 3.5% loan allow me to accept a "gift" for a down payment from a RE partner to purchase a property as an owner occupier." This comment was confusing. If you want the partner to do the 20% down, then it's not a FHA 3.5%. If it's FHA 3.5% you are going to have to live with PMI.
From someone who has beat the bushes here, there are several things you might explore.
Bank of America has a 3% no PMI program. They also told me recently when I was exploring purchasing a cashflowing MF that while they didn't have a product that fit what I needed at that time, they would by mid March.
NASA FCU has a program.
There is a program called NACA. I attended one of their seminars and was seriously underimpressed with their presenter who didn't know their product, but the program may well be solid.
There are ways. Mortgage fraud will get you a room, but you have no choice about the roommate.