Public health insurance is obligatory deducted from your gross salary. From 3000USD you will get around 2100USD (7800PLN). Your family will be insured for free from your insurance. Insulin sponsored by the insurer is very cheap:
As ozil8080 summarized:
When i calculated monthly expenses, it looked like there was a 2000 pln for rent + 500 for utilities+ 800*2 for food + some money for cinema + sports, ended up with around 5000 per month for 2 people to live in a normal life.
So as you see you will be able to even save around 1/3 of the net salary.