Use appropriate blades. I use Diablo D1296L blades for double sided melamine. There are also 10" versions. Lasts about 15-20 sheets, before it needs to be resharpened. New blade from store cuts best. Sharpening company that I use is not doing great job (although they are certified Freud sharpeners recommended at Freud website) because my blades start to vibrate after they sharpen them, and then they vibrate more and more with each additional resharpening. Blade vibration is not good for chipping.
I also use blade disk stabilizer, seems to help.
I get best results when my 12" blade sticks around 1-3/4" above table saw surface (about 1-1/2" for a 10" blade). A little bit higher and I start getting chipping on the bottom side, a little bit lower and chipping starts to occur on the top side.
Bottom side is a lot more sensitive to chipping then top side.
I always buy same types of melamine from same two suppliers and sometimes top and bottom cuts are perfect and indistinguishable from each other, one would need strong magnifying glass to find out which one was top and which one was bottom, other times bottom one visibly chips no matter what.
Sometimes, the sound of blade cutting through the sheet is uniform and mellow, and I know that there would be no chipping at the bottom, other times I hear cracks and snaps that sound like the blade teeth are hitting some hard particles inside the melamine board (like small stones) and than chipping occurs.
If the blade is not very sharp, slower feed speed may help.
I never have problems with top side, it's always the bottom one.
Here are few tricks that could help:
1. I always cut most important parts first, like doors and drawer fronts, when the blade is still very sharp and produces good results on both sides of the cut.
2. Most other parts, like case parts, have only one cut that really matters, and that is the one on the front side of the cabinet. Other cuts are usually not visible from both sides when the cabinets is assembled, and the one that is can be the top side cut, which usually has no chipping.
So, when cutting front side cut, lower you blade to, let's say 1/8", and use it as a scoring blade. Once the piece is scored on one side, rise the blade, turn over the piece and make final cut.
3. If even the new blade would not give you good cuts on bottom side, cut parts oversized (e.g. add 1/2") and use scoring technique from No. 2 for final cuts that will bring the piece to it's final size.
That would be wasting of time for everyday operations, but if it's something that you do once in a blue moon, could actually work.
3. Some people claim they avoid chipping by gluing the painter's tape along the cut area before cutting. Never tried that.
Sometimes, when my newly sharpened blade accidentally cuts through 16GA or 18GA nail or staple it starts making better cuts than before the accident.
Anyway, I would try to repair the scoring blade function if possible. It can lower your stress level significantly by releasing you from dealing with all that "black magic" mentioned above, which I had to endure for 2 years.