C.T.
You're doing great to be daytime potty trained already! My son still wets at night. Our pediatrician said that there is no "blame", "fault", or "behavior" issue here. It is a matter of brain development and bladder development catching up with each other. He said it can be particularly hard for heavy sleepers. Get him up to go in the night when you go to bed or if you wake during the night. Eventually he will get there on his own.
We use pull-ups because I got tired of washing the sheets. If you do keep them in undies you may want to make the bed with two layers of sheets (waterproof pad, sheet and then another waterproof pad and another sheet). This way if you must change the bed in the night it is quick and easy. You just pull off the wet layer and you are good to go.