There have been various efforts to solve this problem for e-mail recently. Mailpile[1] is a great web-based mail client that you can host. It stores mail encrypted and has a very nice interface that makes handling mail encryption easier for users. Protonmail[2] is both a mail service and a nice front-end for handling encrypted e-mail. When a user sends encrypted mail through the ProtonMail interface, the e-mail is sent with a link pointing to a webpage that asks for a certain shared password. They have raised more than half million in their crowdfunding campaign.

Both are very user friendly, very promising, and still in early BETA.

1: https://www.mailpile.is/ 2: https://protonmail.ch/