ATM Machines give Belize dollars. I've never tried to get a cash advance.
I often use credit cards for hotel, rental, excursions and expensive meals. Cash for everything else. It doesn't matter if you have USD or Belize if you know how to divide by 2. I generally bring a good amount of USD as backup but get belize dollars while I'm there, usually from an ATM. I can multiply, but not so good with the division, so it's just easier.
I usually bring home a lot of the USD that I brought with me.