I'm so happy that you're inspired by the block party and want to host one for families. Here's a link to a video on YouTube of a block party in progress. It shows how they set up the classroom, the various kinds of blocks they had, and the different materials they used: https://www.youtube.com/watch?v=lURQpfBqe9g&t=...
While teaching preschool, I hosted several block parties and they were big hits with both kids and parents. The first one I did was a celebration of play and included putting together puzzles, doing finger painting, creating with play-dough as well as building with blocks. I found it to be too much so I simplified it to just blocks the next year. That was much easier and more successful and I liked that the spotlight shone exclusively on block play.
I made poster-boards like the ones that they show in the video, explaining what the parents and kids were gaining from the experience: increasing vocabulary, learning measurement, enhancing communication skills, building teamwork. It was eye-opening for moms and dads as they realized how much block play contributes to their child's social and cognitive development.
Before the event, many of them didn't appreciate that blocks are the ideal STEM toy for young children. Parents who had never considered buying them for their daughters were inspired to do so. Some were motivated to set up play dates for their kids that would feature block play.
The schools in Indiana are big supporters of block parties. If you e-mail a school district there, they may send you more detailed information on hosting an event.