No, I wouldn't accept this.
On the one hand, his reaction is understandable because he doesn't trust you, and with good reason. I think he's reasonable to ask for some things - say for instance, that you stop going to places where you would meet the affair partner, or that you delete the affair partner's number in front of your husband, etc. I also think you'd both be insane not to continue marriage counselling.
On the other hand, tracking you and checking up on you indefinitely is not healthy, for either of you. Either he's controlling and he's now using this as an excuse, or he's hugely insecure and he sees this as the only way to be with you that won't eat him up inside (plot twist: it will anyway).
It's a slippery slope. If you can't go out, how do you do errands, shopping, take the kids out? If you have to sit at home while he goes out, is he going to start suspecting you of having people over while he's out?
It's obviously a hard thing to do, but imo he needs to decide whether he can work on building the relationship back up without this tracking/monitoring, or he can't, and your marriage is over.