Very early each morning, the body releases hormones (from the pituitary) that wake you up and tell the liver to release stored glucose to give you energy to start the day. These hormones also inhibit insulin. The result is that glucose level rises between 4 a.m. and 8 a.m., in a process called the dawn phenomenon. Also, it doesn't matter whether the insulin is injected or is the person's own ... the cells are less sensitive to insulin's effect during this time.
There's another mechanism, called the rebound effect ... The diabetic experiences overnight hypoglycemia, and in response, the liver is stimulated to release stored glucose (glycogen) .. thus, the blood sugar rises.
You can read more about these symptoms
here.
I couldn't find in any of your posts if your husband is insulin-dependent, or on any kind of medication?? There are different treatments, depending on whether it's simply DP, or if there's an overnight hypoglycemia problem. If he's on medication or insulin, these may need adjusting. If he's not on medication ... and the problem is related to hypoglycemia, then a protein-containing bedtime snack is in order, however a snack in the middle of the night would just compound the problem, since the rebound release of glycogen from the liver would already be underway. A bedtime dose of Glucophage (metformin) may be helpful, as this increases the sensitivity of the cells to insulin.
The link I gave you has some suggestions for checking blood sugars during the night, and how to tell which problem is the culprit. Then you can show the results to the dr. who will recommend the best course of action.
Doreen