Is it ok to feed my cat dry dog food between his regular wet cat food feedings?

I feed my cat wet (cat food) food in the morning, afternoon and night. He eats it all within a few minutes and constantly is begging for food throught the rest of the day. My dog passed away a few weeks ago and we still ahve about 20lbs of dry small bites kibble. Right now I will give the cat a small handfull of the dog kibble between his regular feedings. Is this ok for him? He seems to like it, even more than the dry cat food I used to give him.