I have a G1100 router configured in bridge mode. I'd like to have two seperate networks in my home—I don't neeed them to be able to talk to each other—so I'd like to know if I got a switch and connected two routers would Verizon assign both routers public IP addresses, or only one?
You'll need Small business FiOS service along with Static IP service to be able to pull more than one address from the network.
What will work for you instead is to get a VLAN-aware router and then separate the two networks using both VLAN and Firewall rules to deny access to each other's networks. This will allow you to accomplish what you're looking to do while sharing one IP address. DD-WRT and other third party firmware have VLAN support, and you can also consider using products from Ubiquiti networks like the UniFi Security Gateway or EdgeRouter.
Another solution (which costs money monthly as well) is to purchase a secondary residential connection from Verizon treating another portion of your house as an apartment. A single ONT can be installed which has support for two connections (usually deployed to small businesses) or two separate ONTs can be installed.