How quickly you recover probably depends on whether you simply have an exploratory lap & dye, or require surgery at the same time. That said, your DH really shouldn't need to take more than two days off.
I was signed off for two weeks, and needed it. My lap resulted in a salpingectomy on my left side because I had a cyst on my fallopian tube, and adhesiolysis on my right side (where my ovary was stuck to the floor of my pelvis) and I was in a lot of discomfort after surgery. I was supposed to be a day case, but developed acute urinary retention (a quite common complication of anaesthesia, which the hospital didn't bother to tell me about) so needed to be admitted. DH took the day of my lap off, but subsequently had to take the next day off so he could bring me home from hospital once they were happy I could wee again! (Sorry TMI).
After that, I managed quite well on my own, although was in a bit of discomfort, but this was because of the surgery and the fact I then developed a surgical site infection (the entry site around my navel). DH ended up taking a half day off to take me back to the hospital a week later to have the wound cleaned and dressed.
I was very unlucky because I had complications, and I'm sure you will be fine. I do wish the hospital had spent a little bit more time going through possible side-effects with me so I was better prepared when they did occur. They didn't really give me any information at my pre-op assessment; that was mainly about assessing risk of anaesthesia.
I am sure your lap will be straight forward. I was very unlucky. But, that said, DH still only needed 2 days off work initially, and wouldn't have required any more time if I hadn't developed the infection.
Good luck!