The rest of Scandinavia has a similar approach to Iceland, and their economies are ok, probably sounder than the UK actually because people understand that if they want decent public services then they have to pay higher taxes, so the level of government borrowing isn't as high (and they don't feel the need to pay for trident etc which also probably helps), but I digress.
In Denmark the mother gets 14 weeks reserved just for her and the father 2 weeks to be taken at the birth, with a further 14 weeks at full pay that can be taken any time up to the age of 9. This can be taken concurrently with the mother if desired.
Outside of this either parent can opt to take up to a year in total on "day money", basically the same as unemployment benefit, so it depends a bit on how much you earn as unemployment benefit is reliant on you making a contribution to an unemployment insurance scheme, but I'll be getting about £75 - 80 per day when I go on to it (which is of course also taxed!)
Some companies offer enhanced deals over and above this.
In general both parents will take off at least a few months each and it would be considered a bit strange for a father to take no time off at all.
The leave can also be taken as part time working, so for instance you could plan to take 6 months of the year for the mother (14 weeks of which is at at full pay), then maybe 2 - 3 months (plus the 2 weeks at birth) for the father and then the remainder could be spread as a 4 day week for a couple of years.
Of course, childcare is highly subsidised and widely available (around £350 per month for a full time 5 days a week place in Copenhagen), although in some places you may have to travel a bit further to get to a place with a vacancy (maybe even as much as 5km!), but basically everyone wins because employers don't lose their workforce, there's no disincentive to employ women rather than men (who are just as likely to take 6 months off) and parents can take a decent time off without having to worry about the financial consequences (too much), or if they go back to work that the day care is bad for the kids/will swallow up their salary.
BUT, for it to work, you have to have the kind of society that is already organised around it, you could not just introduce it to the UK for instance as the infrastructure isn't there and neither is the political or social will.
It helps to have a strong female participation in politics.
It also helps to have few social inequalities and a well educated population who do highly skilled jobs. And let's be fair, probablythe only reason it works here is because small societies need everyone to be economically active and to produce a future generation of economically active workers, so making it easy to have a family and work is a win-win situation.