We have a production need to join plywood and hardwood edge to edge. We have tried biscuits and dowels with varying degrees of success. We can never get a perfectly flush joint without a lot of adjusting. I would be willing to invest in equipment if I could guarantee a flush joint every time.
(Solid Wood Machining Forum)
From contributor C:
Rabbet the solid piece with the long side under the plywood so there is ample surface to glue. When set up, sand in a wide belt to flush the surfaces.
Let me add that if the two pieces are at different MCs when assembled, you can make a perfect joint that will be imperfect after a few days as the MC adjusts. So, getting uniform MC (actually getting the two pieces to be at equilibrium at the same RH, as the heat used in plywood manufacturing means that it will be a little lower in MC than solid wood at the same RH) before machining is important. Then, once machined, the pieces should not change MC, as plywood and solid wood do shrink or swell differently.
It is also important to realize that if you use a water-based finishing system, the moisture will cause the plywood to swell more than solid wood and the joint will again be imperfect. (Plywood with a composite core will be worse than all wood veneer plywood.) For this reason, we often put a small groove at the joint (scratch line) so that imperfections will not be so obvious.