If you are sending traffic over his router, then he can potentially read into that information. Like everyone is saying, you have to know how to utilize that information, but he will have access. Your options would be to setup a VPN or a proxy, but both of those processes are rather involved, can potentially cost money, and probably won't work with a lot of the sites you visit.
The router being under his ownership changes things, you are a guest on his network, and therefore he has full control over your activity on the network, as he should. If it really bothers you, either talk to him and come to an agreement, drop your devices off of his network, or pay for your own. As a guest, you have no control whatsoever over his equipment, and if you can't come to an agreement with him, then just either deal with it, or buy your own.