Hi Marius
General cost of living is double that of SA. The general trend for prices is they scratch off the R and just put a K...completely crazy. That's for food, clothes etc. local fruit and veg is cheap. To give you an idea....1L long life is K10, bread is K7. Then you get to the other things like baby formula - the big tin is K220. you can get most things here but at a cost and not all the time. Ive gone 2 months without finding tuna in the shops!!
I am in Lusaka so have a bigger variety of goodies. Kitwe is quite a bit smaller and if memory serves me right they have 1 main grocery store which I think is a shoprite (I could be wrong though).
Depending on the age of your kids...there are 3 main schools that expats send their kids to. 2 in Lusaka (Baobab College and the American school) and 1 in Mazabuka called Musakele. Baobab has prices on their website - make sure your sitting down when you read them.
Im not sure of housing in Kitwe but in Lusaka in a nice area for a 3 bed house is about $1500 - $2000. Electricity is a pain so make sure you have a generator as load shedding and general power cuts are common. We get 3 a week for 3 hours at a time (Mon, Wed, Fri 6:30 - 9:30).
You will also need evacuation...have a look at SES. Discovery also covers you if you are only out of SA for 3 months.
That's all I can think of. If you think of anything else just ask