I realize you're not hearing what you want to, but I personally think that there may be a good reason for that.
I have good friends whose DH's seriously are incompetent with their babies because the DH's never step up and offer to bathe, change, rock, walk with, their children, much less take them out somewhere on their own. I personally think it is wonderful that your DH wants to take your DS out on his own for a little bit, and I would nurture that desire. He wants to take care of his child, and he wants to figure things out for himself. That needs to start early, because otherwise your DS might not be so receptive to it later on, especially if you have another child and the whole regression/jealousy thing sets in.
If you're worried about them going to far away, I agree, take baby steps and send them on a walk together. Or you go with them somewhere but then take a walk by yourself while they play at a park or somewhere else.
I fail to see what bad could happen, except that your DH and DS get to know each other better and strengthen their bond. Good for all involved!