The 390 Thunderbird Engine was available in full size Fords from the early 60s. In 66, you could get the 390 GT engine in either a Mustang GT or Fairlane GT (and the Mercury equivalents).
Ford even offered a solid lifter cam 390 rated at 375 Hp, and a 3 duce version at 401 Hp. 406's (428 block, 390 crank) were also offered in limited quantity). Mercury also offered a 410 (428 crank, 390 block) in some of it's cars.
In 1968, a few year end Mustang GTs had the R code 428 CJ (I had one) and Ford won the NHRA Winter Nationals with that car that year. They are very rare, had the Drag Pack option (mine had 4:30 gears) and engine oil coolers. (About 2,200 made, few survived).
A handful of Mercury Cougars were made with Hydraulic cam (the block had to be drilled) 427s before they also went to 428. No Mustang or Mustang GT-500 Shelby's were ever made with the 427 Ford engine (other than experimental cars). The 427 Ford Engine made a few 66 and 67 AC Cobra's legendary.
390 GT motors were actually VG motors, that were handicapped by horrible exhaust manifolds and a transverse muffler. 390 motors were far more durable than 428s due to being internally balanced (428s are external) and having a shorter stroke, the same stoke is used in 390, 406 and 427.
My 68 390 GT was an absolute animal, in one of the lightest cars that could hold a big block. I NEVER lost a race with it, and I raced EVERYONE. It had an aggressive cam, 800 double pumper Holley, Hooker Headers (and mufflers), TRW double roller timing chain, Ford Steel Shim head gaskets (increased compression 1/2 point), Mallory Photo Cell electronic ignition and a HD oil pump.