Generally, SSH will provide you with pretty good privacy - though there are a few pitfalls to be aware of:
First, depending on where you terminate (e.g. the server side) the SSH connection, anything on the other side of it could be watching your traffic.
Second, while the majority of your traffic will be routed over SSH, it is possible (and probable) that DNS lookups could happen outside of the SSH tunnel. That wouldn't give away the full URL granted, but if you are concerned about someone plunking around the server in general this isn't the best idea.
Best plan: Terminate the SSH connection on the network edge where your private server sits. Ideally the database/web server should not be internet facing and requires that you poke a hole through your firewall using SSH to even connect to the server(s).
Bonus points: Using ssh certificates with your connection to further reduce the chance of issues.