it depends on your status in Tunisia. If you're working in Tunisia or retired... if you're working, the healcare system is more than efficient. If you're self-employed or retired then you should suscribe with a private insurance and there is only one who cover at 100%, otherwise you can get any off shore insurance...
I'm retired here and should get health insurance but haven't. I will go back to the US for a Medicare physical and check up this year. I've been here three years. But. maybe 18 months ago I had appendicitis. To make a long story short I ended up at what I think was ony a surgical hospital. He had to be paid before he would operate and later said I had an hour to live (it burst twice but I just thought it was a strained muscel). Five days in the hospital, drugs, surgery, etc. was 1,300 dollars to give you and idea. It was a private hospital with my own room. He spoke only French so he had to resort to one word questions and me one word "oui" or "non" answers. Of course in the USA a night in the hospital is far more than my complete five days here.
Just thought I'd give you a "for example..." I have an Internest and found him by just knocking on his office door. He was the one that had me X-rayed and then told me, "You have to go to the hospital....now." My dentist was a knock on the door too and his office looked like one in the USA but I think he charged me "European prices." He did a fine job. I live in La Marsa
As an expat your company would normally purchase special expat insurance for you as an employee. However, if you are a private resident or retired here then you have the option to buy your own insurance (which is very, very expensive) or use the public system. I have lived here for quite a few years now and luckily I have no major health issues. A few years ago I did need some surgery and I 'interviewed' surgeons (truly). I picked the one who had good English as when I am stressed or ill that is the first language that comes out of my mouth. I was delighted with the result and only spent one night in the hospital.
I do advise though that any foreigner here make sure to go to a private hospital preferably in Tunis and preferably the Military Hospital which is the best in this country. Also ask neighbours and family members who they recommend. In an emergency definitely go the Military Hospital. If it is not an emergency then I suggest that you go and check out the facilities in the local hospitals...........some are not pleasant!
As for dentists, well they don't have the equipment that we all know and love! They are fine for a clean or minor stuff but I recommend returning to your home country or to England (where I go for dental) for major stuff.