Well, your husband has given you the okay for a DADT relationship (don't ask, don't tell). In other words, some relief on the side provided he never has to know.
In these circumstances, I would advise against serious relationships, and only seek casual sex outside of your husband, when you feel you need it. And as he has asked you not to bring it up to him, don't. And do it as little as possible.
It seems likely that he has said that because he was afraid to lose you, but was hoping (is still hoping) that you will never do it. Since you have done it already, it's not an option at this point, but let him think you never will as he wants you to do that.
The fact that you have a specific boyfriend rather than more casual, or even anonymous partners might be a bit of a worry. It might become harder to hide it, and you might see him more often than you would see casual partners. I would be careful about that. Also make sure your boyfriend doesn't expect anything to come out of the relationship, as you don't have your husband's consent for that.
Good luck, and I'm sorry to hear about your husband's dreadful accident.