Julien,
You should never step outside your home country without expat health insurance. If you do, then leave a power of attorney with somebody so they can sell your house back home to pay your medical bills. I have seen it happen...no joke.
Have you travelled on the roads here yet? If you have an accident and are lucky enough to be alive by the time you get to the hospital, then the Medical Air Evac is something that you would pray that you have to get you to Singapore, Hong Kong or Bangkok asap.
The Apollo Hospital is the best one in Dhaka. It is a very well equipped hospital. The only thing that nags me; one would think that any doctor worth his salt will have long since left the country...
As far as treatment is concerned, it is cheap here in Dhaka compared to the west.
Steve