Holla for badassity in parenting! I've been working on this idea of family biking lately also, and I've come up with two solutions.
The first one is the dutch cargo bike. The upside is that this bike can transport four kids plus groceries! The downside is that it is ridiculously expensive. I assume a family sells a minivan and replaces it with this bike. People place their newborns in a MaxiCosi (most popular European baby seat) and put the seat in the cargo hold. The few companies that produce these bikes, called bakfiets, are mostly located in the Netherlands, where they are much more popular. There are bike shops in Brooklyn, Boston, Portland, & Chicago (and maybe others?) that import and assemble them, and I'm working now on figuring out shipping. You can also add an electric assist and make this an eBike, which I will strongly consider if we do buy or make one, since the load will be 200+ pounds. My biking muscles are not that badass yet.
Workcycles.com CargoBike (Great FAQ included in this link):
http://www.bakfiets-en-meer.nl/workcycles-faqs-overviews/overview-bakfiets-cargobike/Brooklyn Rolling Orange Co that imports:
http://rollingorangebikes.com/cargobikes/bakfiets-nl/ $4200 with electric pedal assist
There is a great Instructables about how to make your own cargo bike. This involves welding. Welding your own frame would be much less expensive. I'm considering time involved versus cost. We are living in urban Japan right now, so I don't have access to tools and supplies, but when we move back home to the Midwest next spring, I'm thinking about it...
Instructables on how to build your own cargo bike (welding required):
http://www.instructables.com/id/how-to-build-a-cargo-bike/Obviously, building your own is way more badass. At the moment I’m focusing on building my mothering muscles by expanding my capacity to parent more children for longer hours in a foreign country away from my support network & family. I did, however, finally figure out how to rent an eBike with childseat last week, so we’re leasing one for $30 US a month, and it’s working out pretty well. My 2 year old sits in the front child seat in front of the handlebars, and I wear my 9 month old in an Ergo carrier on my back. When he is big enough (they say 12 months here in Japan), I can upgrade my bike model to a two seat kind with an extra seat on the back. I’ll lose my grocery basket space, though.
Good luck with the biking! Let me know if you figure out any other good solutions!