3500 Euro after tax should net you around 2200 Euro = 8800PLN at current exchange rates.
If it's 14000zl a month (3500 euro - though I'd strongly urge that the salary should be negotiated in zloty and not in Euro) - then unless I'm totally wrong, he should be getting around 9800zl a month - or what, 2450 euro net? That's according to this - money.pl/podatki/kalkulatory/plac/
Is it good enough for a family of 3 with a moderate life style ?
Depends on what you want as moderate. There's no need to pay for underground parking garage, security for the building (Poland isn't unsafe - and while guarded estates are fashionable as hell at the minute, there's really no harm in living somewhere unguarded - probably the nicest estate in Poznan is unguarded, for instance - the guarded ones are horrible places to live - could be different in Warsaw, though).
But yes, it's certainly good enough.
What I'd actually recommend would be renting a place for a month while you get the feel of Warsaw - then you'll know where you want to live and what you can afford. Poland can be incredibly cheap (a monthly public transport pass in Warsaw is 20 euro, for instance) or incredibly expensive - it all depends what you want.