Calculate the child benefit. I don't think the banks include that either. Likewise, various bonus payments. You can then use that for special repayments or other things.
Purely based on salary, I would say it fits. You could also handle the construction on your own. I manage it with less salary too. It really depends a lot on your property and what the construction will ultimately cost.
Just go to a financial advisor and ask what chances he sees for an almost 100% financing.