There's a service sort of like that on i2p. It's a mail server with an i2p address of mail.i2p and a clearnet address of i2pmail.org. You and your trusted associates can connect to the server exclusively from i2p via mail.i2p, and those who have to communicate from the clearnet can still send you mail via i2pmail.org. Assuming you don't send or recieve any personally identifiable information to or from any clearnet e-mails, you can stay pretty anonymous this way.
i2p in general is better than tor imo. It supports e-mail and torrents, isn't reliant on dedicated nodes that could be set up by glowniggers, by default goes through more layers than tor, and it wasn't created by the US government. The only downside is that communication with the clearnet through i2p requires someone to run dedicated services for it, so right now there's no publically-available way to browse clearnet sites from i2p.