Forget a $600k house: consider a house that costs 3 x annual income. IF one exists. But don't buy it now! Keep renting and save, save, save. It's the chance of a lifetime to build up a good cushion, which can keep growing in the background as the eventual kid(s) do.  $200k saved now can easily be nearly half a mil in 20 years, with no further savings! While no on knows where house values are going.
Take the fertility advice here very seriously.  Save while attempting to get pregnant--it could take ages. Only then, consider a truly affordable townhouse. Also listen to the advice about a house purchase and debt piling stress on a marriage. Enjoy the little things now, and in the future. And someday buy the least house you can possibly live with.  It ain't the house that matters--it's the life you live in it. This couple is very lucky with 2 good jobs. Use some of that luck to build a calm and secure future now, instead of rushing to buy real estate in a wonky market.