I actually am going to go against the grain a bit as I think that you're getting a slightly rough ride on here (especially from the person who called you codependent).
The way I understand it is the job is to go and do a certain number of tasks at a site, the tasks vary from site to site. As soon as you've finished the tasks you can go home.
By you helping your husband, you get the tasks done twice as fast and then have a lovely afternoon together.
So for example... your husband is asked to move 1000 bricks from a barrow to a shed. It would take him five hours to do it. Or you can do it together in two and a half hours, and get the afternoon off. The pay is based on completing the tasks NOT the number of hours it takes. And no one would be expected to do more tasks if they finish early.
I can totally understand why you would want and choose to do this - one to split the load which is nice and two to get more lovely free time together.
If someone offered me £30 to wash their windows, and OH and I fancied a picnic later we would absolutely split the job to free up extra time.
But technically people are right and it's breaking furlough rules. That said... it's totally within the spirit of it.
You aren't allowed to work to stop 1) your employers ripping you off (but they aren't because you chose to do it benefit you) and 2) ripping the govt. off (which they aren't because no extra work is done / the company makes no extra money).
It's interesting that the company has okayed it - since they are the ones who could be fined if the government found out. And there's a real coronavirus sneak mentality at the moment so that might worry me a bit in your shoes. (Especially since employers won't be thrilled if you land them a fine).
Also the insurance thing is a big red flag for me: it would be awful if you were injured and not covered. (Only you can know how likely that is).
I see you've decided to stop - and fair enough. It might be better for the reasons above to be within the furlough rules. That makes your original question about the resentment of your day off irrelevant at this point.
You may still want to think about it though. As if you now stop helping the resentment may build further. This is quite natural FYI - I totally resent that my partner isn't working right now when I'm exhausted and working my ass off. Even though I know it's not his fault at all.
Our solution is that he has become "house husband" while furloughed. That means that when I finish we have the evening to do what we like. I still cook because I enjoy it. But he does absolutely everything else house wise etc. So my contribution is going to the office, his is running the home.