Watch the Edges
Melamine, like any material, has its pros and its cons. One of its cons is that it’s prone to chipping when machined and these chips are very noticeable in the finished project. Stack the deck in your favour and use a sharp blade, though that alone is unlikely to solve the chipping problem.
Some of these parts only need a clean edge on one face of the material. An outer gable that will be against a wall will only have its face seen, so any chipping can be positioned facing the wall. For parts like vertical dividers, that’s a trickier situation, as they’re visible from both sides. In this situation I use what I call a “double cut” technique. A scoring blade takes care of this in a production shop setting, but few of us have that luxury at our disposal.
First, a bit of chip formation science. Generally speaking, the underside of a workpiece will chip out as the blade exits the workpiece and damages the lower face. This is in large part because the exit angle of the blade is too close to perpendicular to the lower face of the workpiece. A strange thing happens when the exit angle gets closer to parallel with the underside of the material - it stops chipping. If you make the first pass with the blade set to about 3/16" high, chipping will virtually disappear on the underside of the workpiece. The workpiece can then be re-cut, with the top of the blade above the workpiece. This should drastically reduce chipping, maybe even eliminate it. I’ve also seen people do two half passes with the blade set ever so slightly higher than half the thickness of the material. They flip the workpiece over after the first cut and run the same edge against the fence. Try both approaches and see what works best.
I also like to lightly ease the fresh cut edges of melamine once it’s been machined unless I’m going to apply iron-on tape to the edge. Think of the two sides and one back edge of an adjustable shelf. The edges of melamine can chip easily, unless you ease them. This may leave a very slight gap between mating parts, but it’s much better than medium-sized chips. Easing some of the edges will also greatly reduce cuts on your hands while you work.